Thank you and thanks a lot for the invitation to speak at this at this day, it's a great honor to speak to speak in this event for Barry Mazer. And especially it's a great pleasure to speak on a subject of flat comology. Of course Mazer was one of the pioneers of using flat comology in the arithmetic, especially in his paper on the Wasawa theory for elliptic curves and in relation with Selmer groups and we'll see some points of contact between what I'm going to discuss and what Barry has thought about over the years. So the subject within flat comology that I'd like to discuss is purity, purity phenomena and this is in fact a flat comology analog of what was Grottenich's Absolute Comological Purity Conjecture which was subsequently proved by Gabber and let me just recall a statement of a letter to put the flat comology statement in perspective. So Grottenich's Absolute Comological Purity, now a theorem of Gabber who gave multiple proofs, the first one in 1994, says that if one has a regular Noetherian local ring, regular local ring R with maximal ideal M and if one has a finite etal commutative R group scheme, G, whose order is invertible in R, then the etal comology of this regular local ring R with supports in the maximal ideal and coefficients in this group G which could be for instance Z mod N with an invertible in the ring vanishes for incommological degrees less than twice the dimension of this regular ring R and in fact there is a sharper version which also describes the top degree twice the dimension and above twice the dimension, also vanishes and okay, stated here in the local setting, but if one has a global regular scheme and of course this kind of result says that etal comology classes can be extended over closed sub-schemes of large enough co-dimension in comparison to the degree of the comology class, hence the name Purity and the result for flat comology that I'd like to discuss is an analog of this for flat comology and it has together us with anything else that I'll be discussing is joined with Peter Schultz. So here we have, okay, so we want to drop the assumption that G be etal and that it's order being invertible in the ring and in fact it also turns out to be good to drop the assumption that the ring is regular, to allow that the ring is complete intersection that it's singular but its singularities are complete intersection. So the statement more precisely is that if one has a local complete intersection notarian local ring, R would maximal ideal M and as before, well, we have a commutative finite flat R group scheme G of any order, perhaps of order equal power of the rest of characteristic which probably is positive, then the flat comology which supports the maximal ideal of this local complete intersection ring R and with coefficients in G, flat comology now vanishes in comological degrees less than the dimension of the ring. Okay, so in comparison to Grottenbeek's conjecture here there we were having twice the dimension, now it's only the dimension I'd like to begin right away by giving an example which shows why this occurs in fact it occurs already in the talcomology because we have complete intersection singularities or the order which is invertible on R one still only has the dimension rather than twice the dimension but let me give an example which somehow captures the phenomenon and also in the end are responsible for this vanishing as we'll see in a moment. So firstly by the comological characterization of depth in commutative algebra we have that the comology with supports of this local ring R and with coefficients in the structure sheaf or GA in other words vanishes for in comological degrees less than the depth which in this case is equal to the dimension of R because R being a complete intersection is of course called Macaulay and so if our R is over is an Fp algebra then we get that the comology integrates less than the dimension and with coefficients in say Z mod p or alpha p also vanishes because Z mod p and alpha p admit art and tri are exact sequences for instance like so and by taking and by taking the associated comology along exact sequence from the vanishing supplied by depth we get the vanishing of flat comology with Zp coefficients in degrees less than the less than dimension likewise for alpha p and so this flat comology purity phenomenon that we'll be discussing is really somehow governed by depth in the end at least in positive characteristic and we'll see that in fact in mixed characteristic it's also governed by depth but before proceeding to mix characteristic let's just begin with the case when the carnality of G is invertible in R after all it's not I mean it's in that case it's different depth of R like so one always has so for notary and local ring the comological characterization of depth as in SJ2 is that one looks at this local comology group and it vanishes precisely in comological degrees less than the depth of the notary and local ring and so because our ring is complete intersection depth equals dimension we get we get this and so we somehow in the end we see that our flat comology phenomenon is real coming from local comology it's not enough from UP it's not enough to know the depth reserved for very historic singularities inside it's just from the intersection yes yes I mean then it is also not so difficult to prove for yes okay I mean in this theorem it's really it's important that it's a complete intersection rather than just con Macaulay which we don't see in this example but I mean in fact the theorem fails for con Macaulay and okay it's not all the phenomena that are witnessed in this example but at least we see that it must be dimension rather than twice the dimension okay so now in the case when the carnality of this group is a unit in the ring it was known and this is a result of Gabber who deduces it from from his absolute comological purity here we're dealing with complete intersection before we have we had regular rings after passage to completion our complete intersection becomes a quotient of a regular ring by a regular sequence and by some sort of local left theorem which says that on comology on local comology there's isomorphism in in the range up to the dimension roughly of the ring that we get we get this vanishing from the absolute comological from the absolute comological purity result in the in the regular case in fact there are also other ways to prove it that's also shown by Gabber and the low comological degree cases of this of this of this theorem settle conjectures of Gabber more precisely the cases in comological degrees two and three give the following more more concrete geometric consequences if one has for instance in comological degree two we get that if one has a local complete intersection no theory on local ring r with maximal ideal m of dimension of dimension three precisely three then the Picard group of the puncture spectrum of r has no no non-trivial torsion line bundles so so if dimension is free then the vanishing is in degrees two and two and lower and this local comology I mean this sense this H2 with supports in the maximal ideal for for mu and then somehow translates into into H1 and lower for the puncture spectrum and H1 and lower for a puncture spectrum is sense this and really torsion the Picard group and so from from this vanishing we get we get this we get this statement and just just for comparison let me recall that in SJ2 Grotendig showed the Grotendig-Levschetz theorem that under the same assumptions except the dimension was supposed to be at least for the Picard group of the entire puncture spectrum was shown to be zero so this torsion requirement is not needed if dimension is at least four was was known since since the sixties but there's a there's a refinement in dimension three that allows to get rid of torsion well that shows that there's no torsion and the second the second point conjectured by Gabber in fact in the in the similar in similar vein is purity for the Brow group of in the case of complete intersection singularities more precisely if we have a Noetherian scheme X and a close sub-scheme Z of X of co-dimension at least two oh sorry of co-dimension at least four such that such that the local ring of X at at at Z is a is a local complete intersection for any for any point Z that lies on this close sub-scheme Z then then the comological Brow group of X namely the et alcomology group with coefficients in GM the multiplicative group and torsion coefficients is insensitive to removing this close sub-scheme this close sub-scheme Z the kernel and co-kernel of this kind of pullback map again one somehow can replace GM by mu N are governed by H2 and H3 of comology with supports along Z then by working locally one immediately reduces to this kind of statement and the vanishing of this comology for the degrees two and three with mu N coefficients then gives by globalizing this this global statement of insensitivity of the Brow group upon removing a closed a close sub-scheme or sufficient large co-dimension as long as the singularities as long as the singularities are defined. Okay and so the the because this this case when the carnality of G is a unit in R is is already is already known as settled the main remaining case the main the main case of the theorem is when the carnality of G is is a power of P where with P being equal to the residue characteristic to the characteristic of the residue field of this local complete intersection ring R and this in this residue characteristic is positive and it's and it's this main case that we'll discuss we'll discuss in the rest and what they'll do is I'll briefly summarize the method of the proof overall of this main theorem and then I'll discuss in more detail the aspects of that the parts of that that touch mostly with that have most intersection with with Barry's work over over the years. So since we're we're discussing somehow the bad residue characteristic it's it's no no surprise that that it's a perfectoid methods that allow this advance in the end and in fact there is a part of what we prove is a purity for flat-comology phenomenon in in in the setting of perfected rings and we reduce the main theorem to this to this latter one so let me give let me give a statement let me give a precise statement and for that let me just recall the definition of a perfected ring a commutative algebra type of definition of a perfected ring so a commutative ring a is perfectoid if it is of the following form if it is a quotient of the bit vectoring of a perfected p-algebra for an implicitly fixed prime p by a principle ideal generated by by by by an element by an element psi so it's okay so for so okay so for some here B is some perfected p-algebra the Frobenius and the morphism of it is is a nice morphism perfected p-algebra B and some C which in bit vector coordinates well okay it has its bit vector coordinates C0 C1 so on and this this element C1 is required to be a unit is required to be a unit in a perfected p-algebra in a perfected p-algebra B that's a condition that's just a definition of what what kind of rings will be will be considering let me tell right away that this ring B in fact is determined by a and in fact one can give a definition purely in terms of a rather than B and more precisely this ring B is nothing else than the than the tilt of a in other words it's a inverse limit perfection of the a modular modulo p if one takes a Frobenius and the morphism of a mod p and takes the inverse limit then then then that's that's just our B and B is not your definition B is not complete necessarily complete related to the zeroes coordinate so what happens is that after you complete B related to the zeroes coordinate of this vector you must get this but in general you can have you can start from B which is not complete and then it is not exactly the case okay okay thanks so the C0 added completion of B is just a tilt although I don't I think in the definition one doesn't need to require that BB C0 adequately complete.  Okay yeah thank you all right and this ring then and this ring sorry W I think you're about to tell us. Yeah W is just a it's just a bit it's just a bit ring p typical bit ring of B and in fact it's usually while it's also the can be this I mean it's just notation in the end but somehow it's also the contains period ring a and of this perfected ring a just by definition the bit vector ring of the tilt of the of the perfected ring a okay and another basic fact that is that this element psi is a non-zero divisor automatically that in the end comes from from the assumption that the first bit vector coordinate be a unit okay let me just give two basic examples to have something to have something concrete in mind so firstly if a is an fp algebra then then being perfectoid is the same as being perfect well and in this case C is chest P which in bit vector coordinates is 0 1 0 0 0 and so that in particular satisfies this assumption bit vectors of perfecting module of P is just that perfect ring again and for the converse there I mean for the converse direction of the perfected is of this form is slightly less slightly less trivial but it somehow follows from the fact that any element in the kernel of the of of this map which which satisfies this condition in fact is a generator is a basic property one one proves and the second perhaps more relevant example to what we'll be discussing is that where one has for instance Zp takes out all P power roots of P and then one has some some free variables X1 up to Xn takes out all P power roots of these variables and then we're considering complete intersections with some how we want to quotient by some equations f1 up to fm and when takes out P power roots of these equations as well and and one periodically completes in the end and one assumes here to be able to make sense of these I mean where where where the fi are somehow just for the for the sake of example there are monomials in P and X1 up to up to Xn so that we can take so that we can take P power roots for instance if our if our complete intersection was just Zp and X1 up to Xn module f1 up to fm and the f1 up to fm happen to be monomials like so then some other perfected ring that will reduce to in eventually is some ring of this type of this of this sort of of this sort of form okay and so the main theorem then reduces to the following perfected statement purity in a perfected setting which says precisely that if we have a perfected ring A and we have a closed a closed sub scheme Z contained in the locus where P equals zero in the speck of A such that there exists an A regular an A regular sequence so we basically assume that the perfected A has enough depth along along the Z we assume that there is an A regular sequence A1 up to AD and in A that vanishes on Z so somehow informally the depth the depth of A along Z is at least is at least D that's that's our assumption then in this in the situation the flat comology with supports in Z of of A with with coefficients in any find locally free commutative group scheme of P power order vanishes for in comological degrees less than less than this depth bound less than less than this D so okay so here G is commutative finite locally free A group of P power order okay and in practice this this closed this closed subset Z is just somehow I mean our initial complete intersection will be covered by a by a huge perfected cover in the Z just the pre-image of the maximal ideal will construct that cover in such a way that it has that along Z we have enough depth which will follow from the complete intersection assumption and the enough depth in A and so from from this theorem in the end when one deduces that theorem although I mean there's something in the reduction that I'm definitely not explaining that but this is the key perfected statement that that that one wants and to get this perfected statement we use classification results for such find locally free group schemes over perfected rings these have been shown first in the positive characteristic setting namely in the setting of perfect FP algebras by Bertie Loh and Gaber Bertie Loh did perfect relation in case and Gaber built on his method then by by by Ike allow and Peter Schultz in in mixed characteristic case and there's also ongoing work of unshoots and LeBron who give a prismatic interpretation of the construction anyway the result says that the such g g g g over a g fired locally free group schemes commutative of people or order of a perfected ring a they are classified by their do the modules in particular one can associate them one can associate to them do the modules in the setting of prismatic homology and this do the module denoted by M of g is a module over over a nth of a is an a nth of a module of projective dimension at most one and it's equipped with a Frobenius and semi-linear Frobenius and for Shibong for Shibong endomorphisms and explicitly somehow it's given by the formula as x1 on the prismatic side of this of this perfectoid of of our group g against the prismatic structure sheaf just just like in crystalline do the ne theory in positive characteristic such such find locally free group schemes one can associate them their their do the module given by x1 in the in the in the crystalline site against the against the structure sheaf and evaluated at the terminal object of the of the crystalline site the same thing is happening here in mixed characteristic and this gives an equivalence of categories between between g over a find locally free commutable people order and such such linear algebraic linear algebraic data and in terms of this classification we take this classification and we show the following the following the following formula yeah that's right so in fact I'm not I'm not saying but there are the following there are the following relations that that are required to hold this part is part of the condition work sees a generator of the of the we already seen there is just generator of of the map from a info a back to a of that's rejection and it's okay in prismatic terms is an orientation of the corresponding of the corresponding prism okay and so in terms of this classification we have the following formula for our flat homology that we're interested in with supports in z of the ring a and and coefficients in a find locally free group scheme of commutative commutative with of the power order is given by the homology again with supports in z of of the ring a in of a and coefficients in in the in the in the module and then one takes a fishy boom invariance of this of this of this of this right hand side in homotopical sense so and take some mapping fiber of for shipping minus minus identity so this this formula whose whose profile to some extent discuss in in the rest it allows us to deduce this this this perfected purity and and let's let's see how I mean the point is that since we assume that the depth of a along z is at least d then the depth along z of the in for a is at least is at least d plus one I mean the element psi was a nonzero divisor always and so because a is a quotient of a in for a by this nonzero divisor psi if along z a has depth at least the one has this regular sequence and we can add as a zero tellment of that regular sequence this element psi and one gets depth of a in at least d plus one and so now once one has this depth at least d plus one one once vanishing of this comology in low comological degrees firstly by using by using exact comology sequences one can get rid of for shibong invariance I mean that that's it somehow in the right end at right at the right edge of the exact triangle and afterwards once we'll get rid of that this m of g is of projective dimension at most one over a in so it's so it's a quotient of essentially I mean of projective modules over a in for each of which is a direct someone in the free module and so one one one therefore by the massage reduces to to free modules but one once vanishing in degree one higher and that's where one higher what that's where one higher comes comes from in the end in this fact that size of nonzero divisor and from this key formula it's really it's the depth again that gives that gives that gives that gives a purity of course it is the it is finally presented module of projective dimension less than 0.1 yes yeah that's right all right and so in in the in the in the in the rest of talk I'll discuss the steps that go into proving this key formula star and particularly steps involve proving some new properties of flat homology some some of these properties in some in some special cases of some of these properties have already been considered the major for instance by major for instance in his it was our it was our theory paper on of elliptic curves and on particularly nice feature okay well a nice feature about about the proof of this of these of these new properties is that they actually involve passage to flat homology of simplicial rings and use homotopical techniques in the end and of course it was Mazer as well who pioneered the homotopical methods in in algebraic geometry and then arithmetic with his with his work on at all homotopy joined with my Clarkton so the steps for proving this key formula star is to first to first show it in a case one is perfect in positive characteristic here one uses crystal in do the net theory classification like that which was established by Bertel and Gabber and also written by law and this case is significantly simpler but one one shows it first and then uses this case to derive new properties of FPPF homology FPPF homology with coefficients and finite locally free group schemes commutative and this this derivation in the end it's somehow by reduction to perfect rings and one uses simplicial techniques to get more to get more robust formalism to do those reductions we'll discuss to some extent and finally one uses this one uses these new properties to settle this key formula in general here the techniques that go in are again this classification and the formalism of the Arctopology of Bertel and Matthew so let me perhaps write out more precisely some of the inputs are P complete Arctopology more precisely P complete Arct descent I'll discuss a bit later more precisely what this means for the functor that takes a perfectoid ring A and associates to it the FPPF homology of A with coefficients and finite locally free commutative group scheme of P power order and this P complete I mean the Arctopology is a recent work of Bertel and Matthew that we use that we use okay so let me then proceed to giving those these new properties of FPPF homology that we show along the way okay so for this we'll fix a ring A we'll fix a ring R sorry and commutative finite locally free group scheme G over this over this ring R this will be our coefficients of the flat homology we consider and the first theorem that's used in the proof is excision for flat homology the statement more precisely is that if we have a finitely generated if we have a finitely generated ideal I inside this ring R and we have a map from S to S prime of R algebras and in fact they can be allowed to be simplisher R algebras even this I mean for a moment one can ignore this but in the proof in fact it's very important of simplisher R algebras such that such that this map is an isomorphism along the along the ideal I such that derive the reductions modular powers of this ideal agree for S and S prime for every positive integer N then okay so in the setting the FPPF homology of S with supports in this ideal and coefficients in this group is the same as that of S prime let me just give a concrete example in which this type of situation occurs in which it's particularly useful so for instance in the main theorem in the setting of the main theorem where we have an Aetherian local ring and its maximal ideal then when we consider a flat homology with supports in the maximal ideal of the ring R with coefficients in this group scheme it doesn't change if we replace if we replace the ring by its completion by its maxatic completion in fact it's a statement in special cases that was also used in the wasala theory where flat homology occurs for instance the ring R could be a localization of a number field that's in prime ideal and with okay so alright the second the second property of FPPF homology that I'd like to mention is FPQC descent precisely FPPF homology with such coefficients agrees with FPQC homology and this gives like more robust descent properties larger spectral sequences more precisely the statement is that the functor which associates to an R-algebra S simplitial R-algebra actually the FPPF homology of S with coefficients in G satisfies descent for the FPQC topology and concretely this statement means concretely this means that the FPPF homology of this ring S with coefficients in G is the same as the FPQC homology of course FPQC topology is large for instance that of a field so one needs some cutoff cardinal but that's just the inequality so for every large for every large cutoff cardinal kappa for every large cutoff cardinal kappa we have that the FPF homology can be computed in FPQC topology and in particular if one has a large cover of this S flat cover then one can compute the FPPF homology of S in terms of the check nerve of that cover which is how this result is useful in the in in practice okay and the third property is is descent for yet another topology but after restricting after restricting S is descent for a FPF homology in the P complete arc topology more precisely here one assumes that this group is G that is group G is of P power order implicitly fixed prime P and then one considers a the functor which associates to a perfectoid ring to a perfectoid R algebra S the FPPF of S with coefficients in G this this functor is okay so this functor satisfies satisfies descent for for for a P complete arc P complete arc topology and more precisely what I'll explain the moment what that means what that means more precisely is that if one has a map from a perfectoid S to a perfectoid S prime such that such that for every for every map from S to evaluation ring periodically complete valuation ring of rank one for every such map there exists a diagram there exists another periodically complete valuation ring V prime and a completion of a diagram like so such as such as a diagram commute and this map is finite is faithfully flat in other words okay and this V prime is also a periodically complete valuation ring of rank one in other words one the P complete arc topology is chest topology here in on perfectoids for which any any point of S valued in a periodically complete valuation ring of rank one lifts to such a point of S prime except possibly after enlarging the valuation ring so in particular it's kind of topology insensitive to of course one just for defining it one does not need to restrict the perfectoids and so it's insensitive to reduce structures it's somehow any faithfully flat cover for instance is such cover and so the statement is then that the concrete interpretation of this statement is that the FPPF of this S with coefficients in G can be computed in terms of the cover as the as a derived inverse limit of the FPPF of the check nerve be completed a check nerve of the cover and the point why this is useful is that in practice because the topology is is somehow so weak then in practice one can choose S prime to be a product of valuation rings product of periodically complete valuation rings with even algebraically closed fraction field the nature of the topology allows such covers then once we have this descent result to prove the key formula we can both sides of the key formula satisfy therefore descent for this very weak topology and so effectively we can replace this ring A this perfectoid A by a product of valuation rings by forming suitable hyper cover in the P complete topology and in that case we can somehow almost check it by hand this formula that's roughly how the argument for the key formula goes based on these new properties of flat topology so to which extent is it essential to use the arc topology rather than the previous I think what V topology or the slightly the one where you use not rank one at any so is it for the reductions that you do is it enough to use the V that is you can do things for I don't know I think like in the end one wants these valuation rings V to also be perfectoid and if one has a valuation ring of some really large rank then I mean perfectoid need to in particular be okay I mean in short I don't know right away but I suspect I suspect it's important and in any way it's certainly very convenient for this P complete topology whether one can get away with the V the V descent I not sure okay alright and so the proofs of these okay so in the end we see that it suffices to prove maybe just this statement with that excision and so it's these properties of FPPF topology that in the end give the key formula and so how do we prove this based on the key formula and positive characteristic that we assume there that's a step one so the proofs reduce to the case 1s and s' are perfect FPP algebras okay I mean initially these s and s' need not be even FPP algebras so certainly it has I mean reduction precisely what is what is happening here in the reduction is arg this well if one just looks at a at a functor which computes after inverting P then this functor and here the can be taken to be a topology because after inverting P the group which is of P power order by decomposing into primary parts this is functor so that's why it's descent for the arctopology which is a slightly slightly stronger topology than the P complete arctopology this is a result of bat and matthew which I mean some of the consequences of this of the sarg descent already shown by by Gabber and Fujiwara one also uses deformation theory in a crucial way more precisely the statement from theory that one uses that if one has a square zero thickening square zero thickening S of a ring S bar both simple actually secretly with ideal with ideal I square zero ideal I then the flat the FPPF comology of S with coefficients in G is computed in terms of the FPPF comology of S bar with coefficients in G in terms the cofiber of this map is the r-home r-algebra r-home from the pullback along the identity section of the cotangent complex of this flat group scheme G over A r-home into a shift of the kernel by one like so and in fact it's for this deformation theory where the complete intersection assumption in the main theorem becomes really important because to control this r-home one wants this ideal I to be perhaps free over S bar in practice to be able to control this comology this is a perfect complex supported in the degrees zero and minus one but if the ideal I is some arbitrary ideal this would be for a conmocholering then one couldn't control this deformation here sufficiently sufficiently finally and the third the third input sorry over r I mean r is my base fixed base sorry this should also be r I mean it could also write over S it's not this is somehow object in the drive category of r modules because my group scheme is defined over my basering r and in fact I write in this way so that I don't have to discuss I mean S will be like simplisher learning in the end and so I don't really want to get into what is our home over simplisher learning it's just okay so these two ingredients give some of the reductions that go into the proof of this of these new properties of flat comology but really they by themselves don't allow us to pass the positive characteristic as we want to reduce the perfect p-algebras and the third input is a certain p-addic continuity formula that I'm about to state which which is another property of FPPF that we show so the third in these inputs to the proofs is the following p-addic continuity formula here we assume that G is of p-power order I'll just write it informally like so that G is killed by a power by a power of p and then for a simplisher our algebra S for which for which the 0th homotopy group is Henselian along p so if R is just the usual algebra would know our homotopy then this assumption just means that this S is Henselian along the ideal p for instance so for instance S could be a discrete and pedically complete ring we complete our algebra so under these assumptions the flat homology of S with coefficients in our group G of p-power order is computed in terms of the reductions of S modulo powers of p as the inverse derived inverse limit of derived reductions of S powers of p still with coefficients in G and it's this formula that in the end allows us to pass from something of mixed characteristic really of after inverting p's of characteristic 0 to something that is really a thickening of an fp algebra in the end and it's through this that we eventually go to perfect fp algebras in our reductions and in the remainder of a talk I would like to give a brief sketch of what goes into proving this theorem which somehow will also be illustrative of what goes into proving these properties of fp-pf homology okay so okay so first I mean certainly for simplicity one could assume that S is discrete let's say but nonetheless when it's even in that case these derived reductions they're not really discrete rings unless say is p torsion 3 so it really is convenient to have this extra generality of S being a simplicial ring but to be able to talk about that let me just briefly define what fp-pf homology of a simplicial ring with coefficients in G actually is so first one defines fp-pf side and map f of simplicial rings so these are just simplicial objects in the category of rings say one can think of them like that for just for simplicity say is flat is flat if the following two conditions are met if the map on zero homotopy groups is flat and on higher homotopy which are modules over the homotopy over a homotopy in in degree zero the natural base change map is an isomorphism so the young homotopy map and homotopy group of prime is just the base change of the hand homotopy group of S along the map by zero in other words that in higher homotopy nothing is really happening the whole thing is kind of governed by what is happening in pi zero which where the map is required to be flat and a flat map f is faithfully flat or respectively of finite presentation if the map on pi zero is so then we get the notion of fppf fppf cover in particular a faithfully flat map and we get a site we get an fppf site on simplicity rings that's right I mean I think it's not really a problem like yes somehow really it's an infinity category that's behind this but everything in the end depends on the homotopy category one takes this drive tensor product but the property of the base change being flat or not it really only depends on homotopy group so it's I mean I think it's not so abusive to say it's actually a site but one uses for instance equivalent spectral sequence for the drive tensor product of simplicity rings to show that its notion is stable under base change which perhaps is not immediately obvious okay it's certainly stable under under composition that is clear from the outset and so one defines the fppf homology of S with coefficients in G by chiefifying by okay by chiefifying sufficiently many times transfinately many times just like in Lurie's book on hierarchal post theory the functor which sends a simple shell ring S simply shell R algebra S to the mapping space of to the S point space of G which can be thought of just as a simple shell abelian group and so one places a simple shell abelian group in non-positive homological degrees and then one chiefifies that functor in the infinity categorical kind of sense and so one gets the homology possibly also in positive degrees. Okay let me just give a brief summary of the very basic properties of this process and then we'll proceed to this argument for Piada continuity so firstly in negative degrees nothing happens just like if one forms fppf homology of usual ring coefficients with coefficients in a group or in a shift and in degree zero it's just nothing else but the S point space of G itself. So in negative degrees nothing happens and in positive degrees this one can show meaning it is not it is not immediate from definitions and the fact it's specific to G being a finite locally free group scheme which is the definition of fppf homology and fppf homology okay so in positive degrees this is actually nothing else than just fppf homology of the Pi zero with coefficients in G so this fppf homology of simplisher rings somehow splices this simplisher will be in a group with homology that happens in positive degrees but splices in the ways that's amenable to formalism it's amenable to manipulations in particular taking those R limbs and so for instance one property that one has is that Poznikov towers behave well with respect to this process if one has our S and mapped to simplicial R-algebra SN, SN-1 is such a tower for instance given by Poznikov truncation of the original S the assumption is that the truncations in homological degrees lesser or equal on N are insensitive when passing to SN then the fppf homology of S with coefficients in G is just the inverse limit of the fppf homologies of SN with coefficients with coefficients in G with respect to a tower and it's this property that allows us to get rid of the homotopy somehow in some of the arguments when it's desirable to do so okay so let me get back to this periodic continuity now we assume that SSP Henselian and we want and G is of people order and we want that the R-gamma SG is the same as our limb of our gamma modular well, right properly and there are tons of product formula for H0 and lower I suppose we have lower because ring is simplicial you wrote G of S but this should depend on S if you have a quasi isomorphism simplicial ring this should not change your R-gamma G of S when G is not smooth it's not so natural to evaluate G naively I mean there's a map from this to that and it's a quasi isomorphism it's an interesting isomorphism on homotopy and like Pi H-negative I of this is the same as H-negative I of that which is then really official resolution of something that so if you have a coefficients like mu p or alpha p which is important so you can have a section of this on some scheme which is important but you can resolve the ring of this by smooth things so then you have this simplicial ring with smooth things and then you take G of this but when the group is like alpha p or mu p there are no non-trivial sections so the morphisms when I'm writing G of S it's really a bit disingenuous because it's really morphisms in the infinity category of simplicial rings yes it's not the naive morphism so that's somehow the trick that that's the thing that I'm hiding really that the objects are the naive ones but the morphisms are subtle so you always have to use this yes okay and out of time let me just give the basic basic step is to build starting well first one reduces to chested spy zero by using this postnikov tower argument both sides behave well with respect to postnikov towers because of this fact and then the main some whole step is to replace is to build is to build an in-depth ppf hypercover of S by some SI such that each SI is phenzelian as S was and in addition in addition it has no non-split non-split ppf covers just like one builds local rings in the ppf topology by taking limits overall I mean then one can also for any scheme for any for the ring S one can build in the ppf cover which has no non-split ppf covers itself and if one alternates sets with phenzelization one can make this such that the ring is phenzelian and one continues on the to do the hypercover of the sort this computes the argama of this in terms of the argamas of the SI and for the SI somehow one computes more or less by hand I mean for instance then for SI one has that the argama SI of G because has no non-split covers it's just G of S then one wants to kind of show the same for S modular ppf ppf to the end and then there's only one uses a big array sequence one uses a passage to derive periodic completion somehow derive both the last law anyway this amount of time so I won't enter into details there So I want to go back to a question of of course the G of S there I would have thought of just a simplicial but it's currently not I mean it's in some infinity category is that right? Yes it is a simplicial abelian group as stood as a simplicial abelian group in somehow the infinity category of simplicial abelian group so it's not really like saying that it's a concretely like a physical simplicial abelian group that is not well defined but it's up to somehow But I think a simple approach by hand so to speak is perhaps to resolve your firefight group scheme as usual as a two term complex smooth things and I suppose that for the smooth things some of the manipulations at least if you work at all locally there is no problem of lifting so it should be possible to work more naively like to define G of S at least in the using a time topology as more naively I don't know maybe the world theory needs you but I believe that you can in many cases one can simplify at least for the coefficient Yes in fact we use this kind of resolution heavily in the proofs so for instance the proof of this periodic continuity formula perhaps one can still use it using just by getting a resolution from the outset and without entering the formalism What do you say the proof of? Of this periodic continuity formula I mean it's relatively soft in terms of simplicial techniques that enter and perhaps one can really carry it out from the outset just taking just working in terms of this resolution but for the later ones especially for the excision it is really convenient to have the simplicial rings and especially to have this formula for deformations with respect to ADL I mean it is true that our coefficients in the under are sufficiently simple just a 5 file group scheme or a complex of smooth groups I believe that but also in your continuity thing of course you are using this fancy kind of homology of Luri where you even have to iterate infinitely many times because of this negative homological degree so I'm not so sure about my question but my question was so you write Arlim but I suppose it in good cases so the good cases for example you have an azalean that's a usual azalean ring let's say the p-torsion is even bounded then the situation is like a peak approximation is much better not only Arlim but it is more essentially not exactly essentially but I think that in every homology the projective system will be essentially constant yes in fact it's this I mean we use this type of valkyrie thing in the end of this proof when we have this Arlim and we want that on pi zero for instance so here we have just G of Si which is concentrated negative non-positive degrees and on modular p-torsion we then also show that it's concentrated non-positive degrees we take the Arlim but we still need to show that the pi zero is satisfied with the glypholic condition so that we don't jump off into H1 and to do that we use the l-kick type of argument because the cotangent complex of G is killed by a power of p because it's a and so somehow it's the same type of which is there in this step but the Arlim in general is not essentially constant at least we don't know that okay even so I suppose if you start from a usual language I think it's reasonable to expect that it is


Live from Las Vegas, it's theCUBE! Covering AWS re-invent 2019. Brought to you by Amazon Web Services and Intel, along with its ecosystem partners. Hey, welcome back, everyone. It's theCUBE's live coverage in Las Vegas. Day three, we're wrapping up the show for AWS re-invent. I'm John Furrier. Structuring the signal from the noise. We want to thank Intel for sponsoring this amazing set, two sets here. We had double barrel, cube action, all week, and thanks to Intel, we wouldn't be able to do it and bring the great content to you as today. Thank them for supporting our mission. We're going to wrap up the show with Stu Miniman, Corey Quinn, two experts who are scouring the floor, doing interviews, talking to everybody and myself. Corey, great to see you. It is great to see me, John. Thank you. You're awesome. Got quite a following these days on your work, your business has grown, congratulations. But I saw you running around at the win. You're definitely working hard. So what have you learning? What are you seeing? What's your analysis of the show holistically? I think that Amazon, specifically AWS's product strategy remains what it has been, and that is simply yes. There is remarkably little that seems that it is beyond something that AWS would take an interest in. If you'd asked me to predict what they would have released at Midnight Madness, I would have had several guesses, none of which would have been, well, it's a piano keyboard thing that also does machine learning, and my follow-up would be, well, of course it is. Does it also make fries? And at this point, well, sure, it makes a certain twisted sort of sense. Maybe it's too many days of reinvent in a row. Maybe it's just at this point, a certain level of cynicism that I can no longer escape. But at this point, very little surprises me, but it seemed to be a very AWS event through and through. A volume, the velocity of announcements was at the same levels last year. No real change there. Yes, I am saddened to report that the reinvent house band is still there and has not yet been put to sleep to spare them and ourselves further misery, but we'll see. You didn't like the band? I think the band is a slightly hokey. I would change the lyrics of some of the things that they're singing to at least be humorous. If you're going to go corny, go all in. The guy did nail the queen notes. They're terrific performers. It has nothing to do with that, but it is eight o'clock in the morning. So one has questions. I think the keynote could have been a sleeper if without the band, don't you think? I do maintain that I want an Alexa skill. That is just Andy Jassy reading rock lyrics. I would pay serious money for that. All right. Well, he did put some thought into it too. Your thoughts on the show. Wrap it up, man. What's going on? Look, I mean, the show, as Dave Vellante says, Amazon always delivers with the shock and awe. You know, brought us in deepest. So many pieces here. You know, I took a selfie with many people and the biggest celebrity of the show, AWS Outpost. The rack, it's over in the corner there. And people are asking me about all the gear inside. I said, you should stop asking about that because you will never touch it, only AWS will. So put a curtain around it. It's managed as a service. And that's what I think people are still trying to understand. We've been talking about cloud for what, 15 years now, but Amazon's positioning on cloud is still different than everyone else's. When I think back to some of the waves, there's that buzzword and there's one or two that really architecturally are different and deliver and Amazon laid out their strategy even more and through the geeky pieces and transformation was the theme. Hey Corey, talk of transformation. I met you at this show a few years ago and your special skill back then was wearing a three-piece suit. Indeed.  So my brand and personal sartorial references have continued to evolve. When you're talking about outposts though, you're right. It's the clear star of the show and I love that product so much. Not because of what they say about it but because of the subtext that comes along with that product.  Now, this is going to take a lot of that away.  It's modern-ish. So our cloud buyers naive if they're just going to be buying these solutions from other clouds or prepackage solutions. Is that really cloud or do they care? I mean, what's the difference between cloud native and cloud naive? What's your perspective besides the letter T? Of course. I think that there's a definite spectrum on how cloudy something can be. If you want to just take everything running in your existing data center, virtualize it and then just put that into an AWS region. Okay, great. There are ways to do that and most of them have a VMware price tag tied to them but okay, is that cloud-ish? Is it the best approach? Maybe. I think it's hard to bucket all customers into one.  Like about $8 billion of revenue a year. Why do you ask? There are valid reasons to do a lot of different things and be at different points on your journey. I like seeing Twitter for pets evolve and do the latest and greatest thing. I don't like seeing, for example, my bank doing the exact same thing. I mean, Stu, its beauty of the cloud is in the eye of the beholder. I mean, what he's saying is, and what Jess is saying is, look it, you can't just take everyone and put them into a bucket. It's what you do with it. It really comes down to what you want to do. I mean, John, I go back to what one of the things Werner said on the keynote stage. Everything fails all the time. The difference between the old architecture, which was I'm going to do everything I can and I'm going to throw money and hardware at things to make it enterprise. Well, the new enterprise needs to look like what the hyperscalers have been doing, which is you build for software, which means that everything fails all the time, that our friend the Chaos Monkey will come in here and it doesn't matter what piece goes down, the application needs to stay up running. It's about the application, application developers at the center of what's going on here and that modernization. I really liked Andy Jassy's answer to what I asked him about is, if we go through this cloud adoption, we talk about simplification and people want to buy over solutions, but the successful company of the future will be builders. I got to ask you guys this question. I talked to a friend and I guess I have friends. So he's an IT for a big company. And I said, hey, what do you think? AWS or Azure? And I won't give any way the names, but he says, look it, we don't know what we're doing. Like we're old school IT. We're running a billion dollar business and we have network security. We're classic IT. We know we got to get there. The boss is saying, get to the cloud. And frankly, if we moved to Amazon, half my team would either get fired or they wouldn't get it to work. So we're just going to go with Microsoft because they've been selling us gear and stuff for decades. So there we go. That's Azure. Now that has nothing to do with capability. That's a real life scenario that we're hearing Stu. Corey. It's incredibly important because once upon a time I was a grumpy Unix admin because there's no other kind of Unix admin. And I was very anti-cloud for a long time. The reason was, I could come up with a whole list of limited justifications why the cloud was crap. But the honest answer was is that I had built my sense of identity around the thing that I knew how to do and the cloud felt like it was taking it away from what I was. It wasn't true. There is a growth path. It's not as long as people often think it is, but you can't fight the tide forever and that world is slowly, but surely eroding out from under you.   That's going to depend on where you are, what your constraints are, what your business concerns are. But I also think it's a misstep to view the migration process solely as one of technology. But you- Hold on, I need to chime in here, John, because I think- You can slack in here too because people use that instead of John. Goldilocks syndrome here. There was one cloud out there that you need to be a PhD and the smartest people out here to do it. There is one cloud out there that we're going to meet you where you are and you don't need to make any changes. What Amazon's trying to do is that balance between, we want to make it uncomfortable enough to make the change that you can be successful in the future. Whether or not they've struck the right balance, I think is up for debate and this is a journey. And there are varies out there, but I think- Well, hyperscale- Well, there's two things. Psychology of just the change, right? To your UNIX admin example and my friend, which is true, it's legit. Now the question is, what's the indifference of getting the path? But if you look at the hyperscalers, Dave Vellante points to that all the time, they would spend engineering time to save money. So they'd engineer a solution to save time. Enterprise would spend money to save time. That's the general purpose computing market that used to be. That's not like that anymore. It's not general purpose. The entire theme of this show seems to be aimed much more at Big E Enterprise than the bleeding edge type of story. There was a lot more Goldman Sachs than Netflix, for example. And that's a good thing and that's okay. And there's still room to grow. I mean, they did not announce an AWS 400. There's no mainframe story in the cloud as such yet. That's actually a mini computer, technically. Oh, I'm sure- But proprietary, but proprietary mini computer. You don't want to know what the billing model looks like. If you know what AS 400 is, you're old like us. They call them i-series now, but yeah, that's right, a U-series, done. All right guys, wrapping it up. This is the big, the big point. Final word, Corey. Amazon, long game, still in play. No real impact from competition yet, but they're in the rear view mirror. They're seeing stuff. Did Amazon successfully move the distance between them and the competition at this event, at least from a narrative and or announcement standpoint? Well, I will say that No Other Cloud has a machine learning piano. So I think that that definitely is a differentiating factor and it adds another item to a checkbox list somewhere that someone cares about. But as far as the core competency, I think, Outpost absolutely opens up a world of opportunity for folks who otherwise would not take that step. I think that they are demonstrating a rapid execution story around what it takes to get Big E Enterprise workloads migrated and giving an on-ramp that doesn't require everyone being retooled, reskilled, and oh, everything you're doing is great, but it's awful, throw it away and start over. And Stu, there's trillions of dollars of spend coming in to the sector. Certainly there's clear visibility of the operating models there. There's IT spend, trillions are going to be on the table, up for grabs, your thought. John, it was interesting. I was watching a Netflix documentary, actually about Bill Gates on the way, and talking about what Microsoft went through after the antitrust piece. It is looming right in front of us for AWS.  Absolutely, Amazon has the potential to take a big chunk out of that, trillions of dollars there. It is always day one here. They are always impressive as to the feedback loops, the way they're listening and they're growing. So that was, we said a year ago, it was the Oval Office, the executive office, was the biggest threat to Amazon, and that still is the biggest threat I see. I think the big story here for this reinvent is, Amazon recognizes two things. Big Enterprise needs to transform their way to be successful, to take advantage of the capabilities, not take a transitional incremental improvement, and two, they got competition and they see it. And the pressure's definitely on, they won't admit it, but Microsoft, through their sales machinery, is taking down spend. And if that trend continues, and will Microsoft have the ability to keep that going and not have discontents of scale for taking shortcuts, can Amazon keep the pressure on? Because that to me is the big story, and then it's clear, the narrative is, keep pushing hard and try to extend the lead out past everybody. Whatever the answer is, customers win. Amazon still doesn't use the word multi-cloud. Their architectural design is not to solve multi-cloud, is it is to extend AWS, and it's interesting. We will see which design architecture wins out in the future, but, you know, we... It's a three horse race, they want to be number one, and I think they recognize multi-cloud, they won't admit it, but why would you, if you were building a PC, why would you promote the Mac? It's just like, I mean, and again, if the commercial, who's the Mac guy and who's the PC guy Corey?  It, these days, that starts to become a bit of an open question. There have been fantastic transformational stories. As they say, it's not your grandfather's Microsoft, but then again, Amazon has made some interesting choices as we go too. See, the Mac guy was cooler than the PC guy in those famous commercials. Absolutely was. Who's cooler? Amazon or Amazon?  And it's interesting, Corey, when you look at some of the cultural pieces, absolutely, Microsoft has gone through some transformations, but Amazon was, you know, from, and talking about AWS, they are cloud native. They are cloud. So they are cooler, Vice-Dustin. Okay, depends how you look at it. This is a wrap up, guys. Thanks for coming in, Corey. Good to see you. Thank you for having me. I know you're working hard. Corey Quinn, one of the hardest-working guys in the business along with Stu Miniman, Dave Vellante, I'm John Furrier, John Walls, Jeff Frick, Leonard and the whole team. Thanks for watching, and I want to say, thanks to our sponsors who support our mission, which is to bring theCUBE to events and do as much high-quality content as possible with creators, with decision-makers, with executives, develop, whoever's got the action, the signal from the noise, we get that support by our sponsors. So without them, we wouldn't be here. And of course, Intel had the naming rights studio sponsorship as the headline. So I thank Intel and AWS for supporting these two stages here at AWS. So thank them, and thanks to the entire team for watching. That's a wrap for AWS Reinvent 2019. Thanks for watching.


I'm Joseph Landoffy, I'm the Chief Medical Officer at JFK University Medical Center. I'm also the Division Chief of Neuro-Oncology and Radio Surgery for JFK Neuroscience. I really believe in treating the whole patient. My philosophy is that as a physician we have an obligation to treat the disease that they're coming to us, you know, with. Right now is a very exciting time to be involved in cancer care as a whole. Advances in surgical techniques, advantages in imaging techniques, targeted therapies where we're not treating a breast cancer, we're not treating a brain tumor, we're treating the molecular targets that a particular tumor has. We have an obligation to treat the disease, but I also believe we have an opportunity to lift the spirits.  Even if it's for a moment to see the suffering in their eyes from all that's going on around them, be lifted is worth it for me. That's the most satisfying thing about my job and I think it's important for physicians to know by really getting to know the patient, it goes a long way with regards to their overall well-being in healthcare, not just for the disease that you're taking care of. So I think lifting the spirits whenever and wherever you can is the most important thing. I enjoy seeing patients, I enjoy that patient interaction and I'm blessed with the ability to be an administrator but also be able to continue to care for patients. So it's making a difference whether it's for a patient, a family or the hospital is really what drives me in every day.


What's happening guys? It's Shane here. So a really common comment that I get on a lot of my videos that are about college degrees Are people that are from outside of the US that are just extremely confused about why Americans would spend $80,000 you know to go to college and go on average about over $35,000 in debt just to get a degree that isn't necessarily even going to help them get a job and whenever I've traveled or met Somebody that's outside of the United States. They're always extremely surprised that student debt is such a huge issue here in the US Student debt is running it over a trillion dollars a trillion dollars and it's true The student debt crisis is a huge issue right now You hear about it all the time on TV and it's becoming a bigger and bigger problem And really the only way you can avoid it is by smashing the like button on this video Thank you. No, but seriously, I would truly appreciate it if you did tap the like button It really does help with the algorithm. Meanwhile, there are people who are getting unbelievably rich off of the hopes and dreams of young people In fact education and by that I mean either starting a school or starting a business that has to do with the Loan servicing is one of the hottest industries around right now Whereas people in many developed countries are either able to go to college either completely free or most of it is paid for and Even just a few decades ago college was much cheaper than it is now and going to college and getting just about any degree out There would open doors for you that wouldn't have been available otherwise So in this video, I'm gonna go over the differences between the United States and the rest of the world when it comes to college And how absurdly expensive it is to go to college here And this is why I have the somewhat controversial opinion that if you are going to get a degree here in the United States You should only go to college for a degree that you know what you're going to be able to make money from now in the 1970s the cost of tuition was so low in the United States that you could work a part-time job and Pretty easily pay for all of college without having to go into debt now You might be thinking well Shane, you know inflation has made college a lot more expensive because the cost of everything has gone up And that's a really good thought But if you look at this graph it shows that the cost of college if it only went up as the cost of inflation went up Would only be around $10,000 or so whereas the actual cost of college is nearly three times as much so why the Discrepancy why did the cost of college go up so much faster than expected well in short It's mostly due to a rise in tuition costs as you can see in this graph The US has the world's highest tuition fees now on top of the extremely high tuition fees One third of developed countries completely pay for all of the tuition fees for their students And then another third of them keep the tuition fees extremely low and by low they define that as less than $2,400 a year now one of the most common arguments that I see on the internet when I was doing research for this video is that Education here in the United States is better than the rest of the world and that's why it costs so much more You basically get what you pay for and to be honest with you. You can't really measure how good Education is in one place versus another. I don't think that's actually possible for you to measure it But I think a close comparison that we can basically look at is the cost of Harvard in the United States is about $47,000 a year now Harvard is one of the best universities in the entire world It's easily one of the top three universities in the United States But let's look at a comparable university that is in Great Britain Oxford now Oxford actually ranked ahead of Harvard It was apparently better than Harvard last year anyways, and they're only charging about $11,700 a year. Wow. That's a good message That's less than one-fourth what Harvard is charging for a comparable Education and there's a ton of different examples like this and you know This video is not going to go over all of them because the video would be extremely long But you compare different universities that are ranked around the same and for some reason the ones in the United States are much More expensive than the ones in other parts of the world So again, why did tuition go up so much if our education is about the same as what's offered in other developed countries? Well, if you ask the universities, they would probably justify this by saying that the college Experience in the United States is different and more unique and better than anywhere else in the world After all, they do spend a lot on their campuses as well as different activities that happen on the campus For instance, Texas A&M recently did a $485 million renovation on Kyle Field, which opened in 1927. Are you kidding me right now? And it's true. United States universities do spend a lot more on their campuses. They even spend more on food for instance I can't stop eating But where the heck did they get all of this money to spend on those activities? According to a 2018 study by OECD Americans are spending on average $23,000 per year per student on a category known as routine educational operations Now, this is a very blasé title. I mean, it's just routine, right? But when you look into it a little bit more deeply The majority of that money is going towards the staff and the faculty at the university And this is more than twice as much as other developed countries such as Sweden, Finland or Germany And while you could make the argument that hiring better staff and faculty is going to increase the educational experience in general I think that most people who have actually gone to college would probably argue differently Oh, no! A lot of colleges for instance spend a ton of money on research professors And their job is to research first and basically teach second So they don't even really care that much about teaching They do giant lectures with 300 400 people and I can tell you that at least in my experience and most people I know his experience. This is not a very great environment for learning And it still doesn't explain why it's so much more expensive than other countries that offer a very similar education So the real reason why universities have increased the cost of college in the united states is because they can In the 1990s the federal government basically just gave up control of the student loan program And gave all the control to banks and large corporate entities And by doing this they essentially made student debt and college into a business Now this combined with the fact that student debt is guaranteed by the federal government and on top of that You cannot forfeit it and bankruptcy means that it's very attractive to particular businesses out there And this basically means that colleges had a blank check They could write whatever they wanted on it and the government would be totally okay with it This is especially apparent when it comes to private universities Some of which are 10 times the cost of community college Now looking at that last infographic you probably notice that non-profit private universities were actually the most expensive ones And without going into too many details here just because it's non-profit and it doesn't make a profit That doesn't mean the people who run these universities aka businesses Can't make a lot of money from their salary because any excess profits they have would go towards routine educational expenses And as for the for-profit universities a 2014 analysis by george washington university And nber found that for-profit universities that were eligible for student aid Basically charged 78 percent higher than the ones that weren't Meaning if they could charge more because the government would basically write them a blank check To give the students than they would so it's time to ask the age-old question Who benefits? And go through the age-old process of following the money Now we've already established a little bit that these schools are benefiting Especially the private schools and according to the chronicle of higher education reports A survey was done on private universities and they found that 64 presidents were earning more than a million dollars a year And three of them were earning over five million But who else is benefiting from the crippling debt that students are racking up? Well, it's the people who are servicing your debt, but it's actually extremely difficult to tell who owns your debt Your loans could have been originated by one institution serviced by another Guaranteed by another and owned by yet another so there could be four middlemen Taking their profits off of your student debt Now the majority of lenders are going to be big businesses such as banks third party servicing companies Or government or government related agencies now some examples of the big businesses are going to be discover financial services And wells fargo and company. Hmm sound familiar I'm not going to tell you but if you found out on your own That would be okay. And then we could talk about it, right? And many of these large banks or large companies are actually incentivized to sell your loans to an intermediary Because it basically improves their capital ratio and it allows them to take on even more loans Now to make things even more complicated Many of these student loans are owned by Semi-governmental agencies such as sally may so they're a part of the government, but they're not a part of the government It's all extremely confusing So we've established that they're way higher than they should be you cannot disclose these loans in bankruptcy They're also guaranteed by the government and then on top of all that Some of them have ridiculously high interest rates such as the grad plus loan at seven percent interest And then if that wasn't enough you have to pay a 4.3 percent servicing fee when you first get the loan So more or less what was done in this case is by privatizing the student loan program Which was meant to give americans access to higher education What they ended up doing was creating another cash cow for wall street So basically what they did is they took something that is basically a part of the american dream They made it three times as expensive as it should be and then they made it to where you can't forfeit it It's guaranteed by the government and it costs a lot and you have to pay extra interest on it Now my channel is all about making good financial decisions as well as just good life decisions in general And if you're thinking about getting a college degree if you want to play the game of loans I think it's so important that you make sure that you're going for a degree That is going to lead to you getting a good job Don't go to college for a degree that is not going to directly increase your chances of getting a really solid career It's not worth it. 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What's up everybody, I'm TheMangoose, you are awesome and Project Stamina has announced an estimated alpha release for this summer along with quite a few other updates. If you don't know what Project Stamina is, they are a group of fans devoted to creating a spiritual successor to the game, Gigantic. If this is the first you're hearing about the game, I suggest checking out an introduction and overview video done by Cruf, a fellow YouTuber who did a great summation of the project that is far more current than my own. I'll have that video linked in the description as well as Project Stamina's latest livestream. Today I'm going to be talking about the alpha, some information brought to light during the livestream, and reviewing information I received during a collaboration between Project Stamina, Cruf and I that was done a few months ago. I'll have the various topics time stamped in a pinned comment if you want to jump to anything in particular as well as the social links for Project Stamina that will allow you to track the game's updates, sign up for their newsletter, and register yourself for potential alpha access. First off, let's talk about the biggest news, the alpha. An estimate for an alpha release this summer was announced at the very end of the latest Project Stamina livestream. The team will announce more solid dates and information pertaining to the alpha the closer they are to release. I've been tracking Project Stamina for a while now, and if there's one company that I'm confident in being able to set a firm date and meet it, it's Project Stamina. However, they are building this game from the ground up without having access to pre-made assets the way many of the Paragon successor projects do. Many of my subscribers have been a bit spoiled by fairly polished alphas of late, so I do want to mention that this game will truly be in an alpha state. Think more along the lines of something like early access spellbreak than a fully realized game with a few bugs. Expect to see some placeholder assets and accessible game modes. With that being said, I have played pre-alpha builds of this game, and even in an incomplete state it was extremely fun. If you enjoy gigantic, or if you just want a fun game to experiment with, I highly suggest you head over to Project Stamina.com to sign up for the newsletter which will simultaneously provide your email address to the team, and enter you for a chance to experience the game's alpha. Just be aware that as an alpha tester you will be expected to contribute towards the game's development via bug reporting and providing feedback to the team. I'm looking forward to facing off against you guys on the battlefield and smashing your face off with R4's Mace. Project Stamina also revealed their fifth character, Akka. We've seen some of Akka in the past under his development name, Notch. Akka is slated to be an assassin that employs both ranged and melee attacks. He wields an atlatal and short spear. If you don't know what an atlatal is, it's a fairly primitive device used across the world, but mainly by the tribes of Central and South America.  The spears Akka uses are spines generated from his own body. His left mouse button is a melee attack performed with both the launcher and the spear. His right mouse button will load the atlatal with one of his spines and throw it. This will be a fast-moving projectile affected by gravity instead of a hit-scan snipe. His Q attack is a pounce that deals damage and reduces armor in an area. E allows Akka to spit venom onto his spear that gives his basic attacks a stacking slow. If you throw an Invenom spear, the target will receive full stacks of the slow. He has a passive that gives him a stacking power boost when his abilities come off cooldown, which ties into his ultimate. Akka's ultimate will immediately refresh all of his cooldowns.  I imagine that proper timing of this ultimate will lead to some pretty exciting highlight reels. I like this addition to the game. He's a bit more feral and aggressive looking than the rest of the lineup. We got some new information about the game's quick match style mode called Tribute. The goal of Tribute mode will be to provide people with more casual, short duration games. Two teams will square off in the battlefield and attempt to impress an as-yet unnamed entity by offering Tribute. Tribute can be attained by killing members of the enemy team and planting Shrines. The Shrines will contribute Tribute throughout the match, however they can be attacked and killed. Be careful though, the Shrines bite back. You can also power your team's ultimate abilities in this mode by attaining offerings placed throughout the map. The location of the offerings is indicated by a beam of light reaching towards the sky. An open map with plenty of focal points for battle should provide for a pretty exciting brawl. We also discovered a bit about the as-yet unnamed main game mode. This mode will function along the same lines as Gigantic with a few differences. The Guardians will be known as Goliaths. The Goliaths will be massive inanimate relics that you can bring to life by empowering an entity that will inhabit and animate your Goliath. Gigantic's stamina has gone this route as opposed to the Living Guardians to not only tie in better with the lore of the game, but to also avoid some of the bugs and game imbalance caused by having huge assets traversing normally inaccessible areas of the map. What you see here is an updated UI, however it isn't the final iteration. Valeco talked through some of the examples of the UI and pointed out a variety of features. They are using math systems, that's math, M-A-T-H, to generate the interface as opposed to image assets. I'm a bit lost as to how that works, however I did understand that by minimizing on-screen assets they'll be able to provide a functional UI that displays all the necessary information you need while cutting down on system requirements. What you see is reminiscent of what was used in Gigantic, which makes sense with stamina's game being a spiritual successor. There was some talk of making the UI customizable, however there are other priorities that need to be addressed first before that happens. In fact, Fancy laid it out there and said that most of the features you would expect from a game will eventually be implemented, however they need to follow their roadmap and create the more important components of a functional game before moving on to things like customization. One of the key points that I like to drive home about this project is their attention to creating modular systems that will help optimize the game and increase future production times. They have spent a great deal of time laying out a proper foundation, building prefabricated walls and putting everything in place so that when it comes time to build a house, it's as easy as snapping the pieces in place. Several examples of this type of thinking were discussed during the live stream. As far as art goes, they are currently using and still creating master materials that can be applied and then masked out. This will allow for easier reorganization of map structures while reducing the workload of your GPU. The programming department has been creating templates for everything they do. Character abilities, game modes, how the player interacts with the system, everything. These templates will make it easier to implement anything they want to do in the future. Think of it as writing down a recipe. You could take that recipe and substitute different ingredients to produce different results, but as long as you follow the same basic recipe, it'll be easier and faster to make different kinds of food. For the rest of this video, I'm going to go back into the co-lab that I did with Project Stamina and Cruf. Most of the talking is going to be done by Fancy and Cruf, so enjoy these little tidbits of information from those two. These are called shrines. In addition to scoring kills on the enemy team, shrines passively generate tribute for your team and you can destroy your opponent's shrine for more tribute than you get for killing an enemy player. I think it's three right now. So you see these big beams of light in the sky. These are the orbs. We're still working on a better name for that than orb, but you can collect those. And right now what they do is give your whole team an ultimate charge and we're working on doing other buffs or maybe even just making these be worth points to sort of push the game to a faster end. So if someone wants to grab it. Me. Go for it. Oh, you have to hold it down. Yeah. I'm very greedy. So now my team, and I don't have my ultimate because we haven't put our fours all back in the game yet. My team has an ultimate charge. So Cruf, if you want to like press F. Oh, yeah. So that has like a big AoE knockback. And now that we have these big beams of light, you can see where the next orb is. Looking up into the sky. Quality of life. Nice. That's what I call quality of life. So crew of flit mangoes get this one. Oh, the the new effects for Matani. Very nice. Yeah. Yeah. You can thank Killboy for that. He's the one running around. He's our lead engineer and is the one making sure that the servers stay running. And yeah, he's been he's been starting to spin up some VFX in a spare time and they're looking really good. Can we see that again, Killboy? He's not in this chat. The crew has it, too. It's the button on Q. Yes. Whoo. Right. And they're pretty bad. That is Matani's Wind Walk. It speeds up allies and slows down enemies. And mangoes, if you want to see some of the latest results of our VFX, go ahead and fire your ultimate. I'm scared. OK. Oh, OK. Oh, wow. Oh, that did a lot of damage.  Very nice. I like that. As you can see, we are both passively generating tribute for our teams right now. So even if we're just like turtling in our own bases, it does push the game towards an end, which is nice. Oh, I just made them all. That's OK. More orbs spawn pretty quickly. And you can track them down via the lights in the sky again. Very nice. Exactly. So one of the other things that we put in since you have last played is we don't have the selection process built into the menus yet, but we have the base Omen ability, which is the Super Jump, and you can get that on R. OK, so everybody has the. So that's only if you select that Omen for Super Jump, right? That will be how it works in a future version. But right now, you just automatically get Super Jump. OK. In the future, we'll bring more of the other Omen online and have a selection screen for them. And so Omen's are something you select before the match to empower your character to either increase their offensive power or maybe shore up some some of the weaknesses that they may have. Yeah, or even like do something really specific to synergize with your team. Like, you know, they're they correspond with the. The Celtic and Nordic Ruins, which are an source of inspiration for some of our games, lore and magic systems. And so just in the Elder Futhark, there are 24 of those. So we're looking at eventually this is probably not until post release having 24 different abilities to select from. But for now, it's just Super Jump. OK, and I do see that it. That is in the middle of my bar that does go on cooldown and then fills back up to let let me know when my Omen is off cooldown. Correct. Catching on maybe also other aspects of a game and other quality things. Do you guys have any information or updates about audio design or music, things of that nature? So we're really slow rolling audio and music. We got asked this about this in the in the public discord recently. So it's it's something that we're very aware is on people's minds. But we're going to be using a a piece of audio middleware that actually. That responds to a lot of very technical and unique game state information. Like it will. And this is not a system that we are designing. This is a system that we are going to acquire and build into our engine. It's like ready made for Unreal 4. So it's going to be like a plug in and a consultation with with an ambassador is their program's description of who these like who people that help on board new studios are, but it will like pay attention to the geometry of a map and provided you've like set materials for. Oh, you're standing on stand. Oh, you're standing on stone. So you're going to be able to do that. Set materials for. Oh, you're standing on stand. Oh, you're standing on stone. So your footfalls sound different. It will map like what direction people are in and. Like how many like how many corners sound has to bounce around and. Automatically change, you know what you're getting in your headphones based on like math geometry, which is super cool. And then the music is going to run on a like dynamic state based system. So as you get into a fight with more people, the music, the intensity, the music ramps up and then when you run away and you're on the other side of the map and there's nothing threatening you, it ramps back down to just like some ambient sound based on the map. And that's like a lot. Yeah, work. I can imagine it's a really it's a really unique style of composition that even a lot of very experienced game composers don't necessarily do because most games don't need that kind of thing. You know, it's a very specific ask of. A game to need. State based music for so many different states. And it's pretty much only like a versus multiplayer thing. So it's not, you know, like Final Fantasy has brilliant music, but it's all.  Oh, it's the it's the main character's theme. Oh, it's the sad time. Let's play the sad time music. And they're they're they're brilliant pieces, but they're not written to be like deconstructed and reconstructed in layers so that so that they they can come apart. Oh, we hit 40 points and the game ended. Game. Oh, that was a game in condition. So that's where we're at with music. Our sound engineer is quietly putting together a bunch of stuff and quietly. That's ironic.  And I don't I guess I haven't told you this directly. But your your audition showed the exact kind of brass that we cannot possibly look away from. So I am I am actively talking to our sound engineer about getting getting an announcer pack with your voice in it set up proof. Good job.  Provided you are like everybody else who puts anything into this project willing to work for free and the joy of knowing that you contributed to a game. Absolutely. Congratulations, crew. Oh, my God, my party. I'm so glad I bought cake today. I'm going to have a slice. Speaking of cake, good transition, crew, why don't we talk about cake a little bit? Oh, OK, so cake is our Patreon created character. We've been working on this design as we the Patreon community has been working on this design for over a year. And they've built a kit that I think is really awesome. It's definitely not something that I would have built, but the way that it shook out looks like it's going to be a lot of fun to play. What I can say, because if you're paying a lot of attention to how we do things, there's a lot of symmetry in all of it. The one class that we don't have covered so far in our in our exist in our announced roster is a caster. And the one faction that we don't yet have two characters from is the Melanarch. So cake is a Melanarch caster. And they have their their kit is designed. It's really cool. And we also built in one upgrade to resolve a tiebreaker on their on their like mobility, utility ability. That was fun to say. It sounded good to the ears. Thanks. And we're working on on visuals for the character right now. So what the patrons are seeing is a week by week walkthrough of the project stamina character design process right now. There's there's too many like really nuanced and hard to define scenarios to account for in the artistic side of character design. You know, we have to look at how does their silhouette fit in with the existing cast? Is it like portraying the personality of somebody from the Melanarch correctly? Does it fit with our game world and our lore? And that's just not stuff that I'm prepared to put to a vote because I don't know how like game design is something that I've been working on very intensely for about a decade now. And I'm like prepared to break down the process of designing a kit. Artistics is something I can give input on, but it's not something that I lead. That's why I have an art director that's not me. So the the polling portion has stopped for now because I can't put it to vote and still guarantee something that is the best possible thing for the game like I could with the way that we were designing the kit together. But it's looking awesome and we're really excited to share more about it. Um, as it nears completion, I I'm trying to really give the community as much ownership of this as possible. And that includes how we handle the PR around it. And so far, the community has voted to mostly keep things really under wrap and do a big reveal all at once, which is kind of a shame for me because if we were talking about it more, more people might get interested in the Patreon and like join, which is good for our bottom line, clearly. But I don't want to take agency away from the people that have already signed up to kick a couple bucks our way. So that's the way we're doing it. Good to hear. Are you guys queued up, by the way? Oh, no, I'm just sitting here at the main menu. OK, thank you for three minutes. But yeah, cake is really it is really fun. If you guys didn't know, don't know, I am a Patreon supporter for Project Stamina and I have been voting on cake. I'm not as into it as a lot of the other people are. I'm more of a hands off. Let let, you know, nature take its course, let everybody I think with the the server party kicked us out there. But yeah, I'm more of a hands off sort of guy. But yeah, if you do want to get involved with with the creation of a character, it is a vote process. Some people get their feelings hurt a little bit when when the thing they want they want doesn't get voted for and but, you know, and other things that they do want does get voted for. And then they feel really happy and they get to see that in the game. And it's really fun to to affect the the the development process of a character. Everybody always has their own hero designs that they want added into a game. And this is a fun way of doing it with an entire community. Is the character's name actually Kate? No, no, I was like, that's an awesome name. Kate stands for and this is like just to just to show how much we can we can close and re queue by the way. Just completely close the game out. Yeah. Yeah. Oh, I was I was. So this was actually a patron's suggestion that we call it cake. It stands for community architected kit experiment. While the alpha for this game is just over the horizon, there are still some things that need to be completed before we can get this one in our hands. Project stamina still needs to build in character stats with unique modifiers, add in more status effects, introduce a practice arena and build the last set of characters. All of that, of course, will take some time. However, the momentum of this project continuously increases. The more they do, the better they get at doing it. The better they get, the faster they get. I truly hope the project stamina is successful in their endeavors. Yes, they have spent the time to lay out the tracks and their train is currently building momentum, but there are outside factors that can derail even the most well built engine. This is where we come in is up to us to keep encouraging the team, letting them know that we appreciate their efforts and spreading the word about the project. If you have the ability to do so, hit up their Patreon and support the project monetarily. Financing the game is appreciated and necessary, but what they really need are the fans of this game to keep pushing them forward. You don't need to be a patron to support the project. You just need to be involved. Be there for them because they're trying to do something special for the entire gigantic community. For now, this is the man goose signing off. You guys have a good one. A man goose. Quick question for Kroof. OK. Have you noticed? I'm on the spot. Have you noticed that I didn't notice this for frickin ever? Have you noticed that R4 really has one arm? I did. I didn't notice it. How did you not notice that? I don't know. It seems so ridiculous now that I know. I mean, he could like a really small arm that's like under the game. You never know. It's just like just a baby arm. There's it's just it's just a hand. There's no forearm. There's no upper arm or shoulder. Please don't give me a baby arm. There's a hand where his shoulder socket is. That's cannon. I'm now a writer for the game. You're welcome. That's what his charge is.  Oh, my God. Yes. He has a really hard time opening jelly jars.