Please René. Thank you very much. So I want to speak about abelian varieties over Q squared with 97 with good reduction everywhere. And before doing that, let me put this in a little bit in a context. So the big theorem in this subject is a theorem by Abrashkin and Fontaine. They proved in 85 shortly after Falking's proof of the Mordell conjecture that there is no non-zero abelian variety over Q with good reduction everywhere. And to explain what kind of result this is, let's look at the case of elliptic curves over Q. So an elliptic curve has a Weierstrass equation. You can find one with coefficients in Z. And you can find the so-called minimal one in the sense that it has the best properties when you reduce it modulo primes. Then this minimal Weierstrass equation has a discriminant, which is a complicated expression, polynomial expression in the coefficients. And this discriminant is 0 modulo p precisely when the reduction is bad. So if the reduction is good everywhere, then the discriminant is not divisible by any prime. And therefore, it is equal to plus or minus 1. And this is a di-authentic equation. And the statement then that such elliptic curves do not exist says that this di-authentic equation doesn't have any solutions. And that's the kind of statement it is. It says that a certain di-authentic equation, it's this discriminant equation, doesn't have any solution. And this theorem has been generalized to not only two abelian varieties over Q, but also two abelian varieties over some or other number fields already by Fulton and Abrashkin, for instance, quadratic fields. And I want to try to generalize it to real quadratic fields today. And that is a nice family of fields, because then in general, the statement is false. So let me explain how you can construct the abelian varieties that have good reduction everywhere over real quadratic fields. So you can make them with modular curves. You take the covering x1 of delta over x0 of delta, where delta is the discriminant of a real quadratic number field. Then there is a quadratic subcover. And then you take the, that's a curve y, and you take the Jacobian of y, and you take the quotient by the image of the Jacobian of x0 of delta. This is an abelian variety. And you can show that it is isogenous to a product of two conjugate abelian varieties over Q squared of delta that both have good reduction everywhere. So that is an example of an abelian variety with good reduction everywhere for every real quadratic field. But it may be that this abelian variety is zero. And then still you may hope to prove the theorem. Again, the generalization of the Brashkin Fontaine theorem. OK, so now I will show you a table for all the discriminant less than 100 of real quadratic fields. Here it is. And here's let me, OK. So the dimension of this abelian variety A on the previous slide grows roughly linearly with A. And so you see here columns, columns with discriminants, and next to it the dimension of this abelian variety A. And you see that in the first column the dimension is always zero. And in fact, the little blue V that you see there means that in that case one can prove, I ever prove that there do not exist any abelian varieties over that real quadratic field with good reduction everywhere. The potential counter example has dimension zero. However, you see in the other columns that the dimension grows. And then, in fact, the theorem is false. But then when you see a little V, that means that I can show that over that real quadratic field, the counter example that I just constructed is the only one. Apart from powers, you can, of course, if an abelian variety has good reduction everywhere and you take products with itself, then that abelian variety also has that property. But apart from that, it is the only example. So this then can be proved for discriminant 24, 28, 29, 33, and the other ones that have a V here. And there are two colors. So the V is blue. I can really prove that. And the V is red if I can pre-prove it under the assumption of the generalized Riemann hypothesis. I should say that the larger values of the discriminant here have been proved by Lassina Dembele. This is all joint work with Lassina Dembele, as you could see on the first slide. And in fact, two of the blue Vs here are also due to him. I needed the Riemann hypothesis, and he was able to avoid it. So in all the cases where there is no V, I do not know what happens. Whether this abelian variety is the only one or not. So today I want to speak about the case 97, the largest case. In that case, the abelian variety that is constructed by means of this modular curve has, as I mentioned, three. And the theorem that I want to discuss today is that that is the only abelian variety with good reduction everywhere. Apart from taking products with itself over q squared of 97. And the way this is proved is the same way Abrashkin and Fontaine proved their theorem. What we do is we look at the torsion points of an abelian variety with good reduction everywhere. And we show that the torsion points are forced to have a certain structure. And it is unique. And therefore, there is a unique abelian variety. And the torsion points are points of the abelian variety. And they are points of group schemes, of the group schemes of torsion points. And so let me talk a little bit about finite group schemes. So I fix a prime number p. And I will look at p torsion points or more generally torsion points of order of power of p. So they form groups, groups of points. And they are actually the points of group schemes, beautiful group schemes. They are finite and flat over the ring of integers. So the main example in this talk are, as I said already, p to the n torsion points of abelian varieties with good reduction everywhere. But there are also other ones. There are, for instance, the roots of unity group schemes. There are constant group schemes. And the z mod p to the nz is the main examples. With group schemes, you can do all kinds of constructions. You can take just groups. You can take sums. You can take subgroups. You can make quotients. There is also a notion of duality, Cartier duality. These group schemes are dual to each other. Z mod p to the nz is dual to mu pn. And it is fine to think, if you are sort of not used to working with group schemes, just think of the Galois module of their points. So the group scheme is just the points, except that it has an integral structure. It has a scheme structure. And in fact, if you consider group schemes over a field, rather than the ring of integers, then it is actually the same thing. The group scheme is completely determined by its Galois module of points. So the points together with the action of the Galois. There is also a notion of a simple group scheme that is a group scheme that doesn't have any proper subgroup schemes, close subgroup schemes. And you can see this on the Galois module. So the notion of simple coincides completely with that. So let me give you some examples. So maybe the easiest example is the group scheme of p roots of unity. So p roots of unity are given by the equation x to the p is 1. So the algebra of this group scheme is this ring here. And the group law is just multiplication of roots of unity. So that's the group scheme. And the Galois group acts on the roots. Another example is the constant group scheme. So here you can write down an algebra where the points have p coordinates. And it looks like this. I will not write down what the group law is. But if you look a little bit at the equation, then you see that over a field xi is 0 or 1. And therefore, the Galois action is trivial. So this is another example. So the third example are mu 2 and z mod 2. You see that mu 2 is over a field plus or minus 1. And z mod 2 is constant. It is 0 and 1. And in both cases, the Galois action is trivial. But the group schemes are not the same because the rings are different. So this is an example where the Galois modules are the same. But the scheme structure is different. That can happen. Here's another example. Just you see a group scheme. It's just you have equations for the points. Here in this case, there are two coordinates, x and y. These are the equations. And if you solve them, then you see that over a field, you have four points. You see, this says that y is 0 or 1. And if you substitute that here, you find what axis. There are four points. You can check that this fancy formula here gives an addition law. And this is an example of a group scheme of order 4. If you put y equal to 0, you get the formula x squared is 1. And then you recover the subgroup scheme, which is isomorphic to the roots of unity, to mu 2. So you have mu 2 is a subgroup scheme. And in fact, you can compute its quotient, which is z mod 0 2. Is that a question? No, Rene, please continue. OK. So now you have exact sequences of group schemes, just as you have for Galois modules. Here's an elliptic curve example. So if you take this elliptic curve over q squared root 41, you can compute its discriminant. And you will see that it is a power of the fundamental unit, epsilon. So it has good reduction everywhere. So all its torsion points subgroup schemes are finite and flat. So let's look at the two torsion points. There are four of them. Here you have the four points. And the Galois action is trivial, you see, because epsilon is in the base field, is in q squared root 41. And you see in elliptic curves, the neutral element is always at infinity. So you don't see it in this equation. But a point becomes the point at infinity modulo prime. It reduces to the point at infinity modulo prime if it has denominators at that prime. Then it goes to infinity. So you see that 0, 0 does not reduce to infinity modulo any prime because it doesn't have any denominators. And that means that the constant g modulo 2 is a subgroup scheme. And again, you can compute quotient, which is mu 2. And well, it is also true that e2 is you can also write it in another way as the product of two group schemes, which I wrote down below. And this is just to show you that these group schemes, they are like modules.  And group schemes are not. And here you see something that can happen is that you can have two filtrations with simple subgroup schemes, but that are different. OK, now my plan is to first briefly go over the proof of Fulton and Abrashkin over q and then use that experience to explain you the proof over q square root 97. So in order to describe what Abrashkin F Fulton proved, I introduced the root discriminant of a number field. So that is the discriminant, but you have to take the dth root of its absolute value, where d is the absolute degree. So that is a positive real number, and it is the root discriminant. And what Abrashkin F Fulton show is that if you have a finite flat group scheme, a P group scheme, and you join its points to a number field, then while it is known that the extension that you get then is unremifed outside P because the reduction, not because it is a finite flat group scheme, but it is remifed at P. And what they show is that the remifed at P is also very moderate. And this is expressed in terms of the root discriminant. So and it is especially moderate if the group scheme is killed by P. So if it is a P group scheme killed by P, for instance, P torsion points of an abelian variety with good reduction everywhere. So the statement is that then the root discriminant of this field is at most the root discriminant of the base fields times this expression in P. For instance, if we take the base field Q, and we take P equal 2, and we take a group, let's take a simple two group scheme. If it is simple, it is automatically killed by 2 because otherwise the two torsion would be your proper subgroup scheme. And so if it is simple, it has to be the whole thing. Then G is killed by 2. And then the theorem says that the root discriminant of the field is at most 4. So this is a very spectacular statement. It means that if I have such a simple two group scheme, even if the order is 2 to the million or something, if then still the points generate an extension that has very little ramification, the root discriminant is at most 4. OK. And now we confront this with Othlisco discriminant bounds. So Othlisco in the 70s proved certain bounds for root discriminant. So he showed that if the degree of a number field is large, then the root discriminant is necessarily also large. So he exhibited an explicit, well, explicit, rather complicated explicit function F with the property dysfunction here with the property that if the degree is large, then the root discriminant is also large. And this function is rather difficult to compute. So there are tables around that you can find online. Here is one. So here you see the degree on the left in the first column. Let's ignore the B. Then this is the lower bound for the root discriminant if the field is totally real in the third column. And in the fifth column, there is the lower bound for the root discriminant if the field is complex, totally complex. So you see, for instance, that 4.5, then the degree, if the degree of the number field is 5, then r6, then the root discriminant is necessarily larger than 4.5. So if you go back to the statement here, it means that in this example where the root discriminant is at most 4, I know that the degree of that field is at most 5 because of the bound by your list code. The bounds in the totally real case are even better. The worst possible case is the totally complex case. So here I repeat that again. So if the field is q and I look at points of a simple two-group scheme, then the points generate a number field of root discriminant at most 4 and therefore of degree at most 5. So that is even more spectacular. Even if you have a group scheme of order 2 to the million, then its points will never generate an extension that has degree more than 5. And you also know that that field is only ramified at 2. And then with a little bit of class field theory, you can actually show that not only is the degree at most 5, it must divide 4 because there are no odd degree extensions of q that are only ramified at 2. You can prove that with class field theory, for instance. But then it means that the Galois group acts on the points of such a group scheme through a group of order 4. So then we have a two-group that acts on a two-group and then two groups that act on two groups always have fixed points. So that implies that the Galois group has a fixed point. But it was simple. We said the group scheme was simple. So there cannot be fixed points until everything is fixed, unless everything is fixed. But then it must have ordered 2. So I prove now here that the only simple two-group schemes over z are only 2. It is z modulo 2, the constant group scheme, and it is mu 2. That follows from general results by or state. If you know the order is 2, then you also know the structure. Now that implies the simple group schemes have order 2, and they are those two. Just as with Galois modules, every finite two-group scheme, you can cut it in simple parts. You can filter it with subgroup schemes, and then the successive quotients all have order 2, just like with modules. And so knowing the simple pieces tells you a lot about the structure of these two-group schemes. And what, in fact, you can do is you can use this by more or less classifying what these two-group schemes look like. And you can, in fact, show the following. You can show that they are always in an exact sequence like this. And how do you prove that? Well, you say they admit some kind of a filtration with simple steps. So I visualize that here. So these are the successive subquotions. So they are in some random order, a priori you don't know. But now you can prove, and I will not go into this. It follows, essentially, from the fact that the class number of q is 1. You can prove that any exact sequence of this type, with z mod 2z on the left and a mu 2 on the right, necessarily splits. And that means that in this filtration, if you have a z mod 2z on the left and a mu 2 on the right, then you can switch them. You can modify the filtration and switch them. So and if you do that for all the z mod 2z's and all the mu 2's that you see, then at the end of the day, you can push all the mu 2's to the left. And you can push all the z mod 2z's to the right. So then on the left, you have an extension of mu 2's. And on the right, you have a successive extension of z mod 2z's. Now, the extension of z mod 2z's is et al. And then therefore, it is determined by the action of the Galois group, which is unremifed. But q has no unremifed extensions. Again, I use that the class number is 1. So this is constant. And similarly, this extension is diagonalizable. So it is next, yeah. So that is exactly this statement here. So here it is again. I have this exact sequence. This is constant and this is diagonalizable. Now we apply this. Now I go back to the proof of Abrashkin and Fontaine. And I'm going to show that there cannot be an abelian variety with good reduction everywhere. So let a be an abelian variety over q with good reduction everywhere. I take it's not it's two torsion, but it's two to the end torsion. So this is a finite group scheme, finite flat group scheme of order of power of two. And I apply what I just proved that it fits in an exact sequence of this type with this one diagonalizable and this one constant. So I, oops, I get a sequence like this. Now, the idea is that this constant part, if I reduce it modulo prime, it remains constant. And I get constant groups, I mean, the Galois action is trivial and the points do not go to zero when I reduce them. So constant group schemes give me points also modulo p, rational points. And the idea is now that over a finite field an abelian variety cannot have too many rational points. And but the problem is it may be that this one is trivial and everything is here. So then the constant part is very small and I cannot use this argument because all the points are here. In order to get around this, I take the dual of this sequence. So this sequence flips around and the dual now of the constant becomes diagonalizable. The dual of the diagonalizable becomes constant. And the group in the middle, the Cartier dual of the two to the end torsion points are exactly the two to the end torsion points of the dual abelian variety. So I have a similar sequence. And now you see this can, if this is very small and n goes to becomes big, then this must be big. And therefore this must be big. So either this one is big or that one is big. And now I can make my contradiction because I take the product of these two sequences. So then I get that Cn times mn dual, it embeds in this abelian variety. When I take the isorgeny, I divide it by mn and here I divide it by Cn dual. So I get this product, the product of these two constant schemes embeds in the product of two abelian varieties. This one modulo mn and this one modulo Cn dual. And now I get my contradiction because I know what is the cardinality of this group scheme. It is the cardinality of the two to the end torsion points which is to the power two ng. It is at most the number of points of the abelian variety over a residue field. You can take any one you like. And that is since these abelian varieties are isogenous to the original abelian variety and since isogenous abelian varieties have the same number of points, this is at most the number of points on the abelian variety over Fq squared. And now I have a contradiction because this is constant. If once I fix q, this is fixed and here is n and this goes to infinity. So this cannot happen unless of course the dimension of the abelian variety is here. Yeah. So this is how it, how the proof, how it goes. Okay. Now I go to the topic of the lecture of today after having given you this example. We go to square root 97. Okay. So there we have this three dimensional abelian variety that is in the modular curve that we make with modular curves. And let's first look at this abelian variety a little bit. You can associate it to it is a Hilbert modular form and I wrote here the Hecker eigenvalues of the first few coefficients, the prime ideals P are prime ideals of the ring of integers of q squared with 97 and these are the ones that have the smallest norm. And then the coefficients of the Hilbert modular form are this where alpha is data nine plus data nine inverse. So this already shows that the Hecker algebra which has ranked three over Z must be equal to two Z alpha. So that is a PID. It is the ring of integers of the real subfield of q zeta nine. You can compute once you know the Hecker eigenvalues you can compute the characteristic polynomial of Frobenius for the first few prime ideals. Here they are. So they are of degree six because the abelian variety as I mentioned three and this is the characteristic polynomial of the matrix that acts on the P torsion points for every P. Okay, from now on I will call my field q squared with 97 and I will call it F. And so the ring of integers is this ring. And let's look a little bit at these characteristic polynomials and I will work with two torsion points of this abelian variety. So I'm interested in the action of the Galois group on the two torsion points. So the characteristic polynomial then is this polynomial taken modulo two on the two torsion points. So I ignore the first because two is two so I take another prime. And if I look at this polynomial modulo then you see that I get t to the sixth plus t cubed plus one. And that we recognize as the nine cyclotomic polynomial. And that means that the Frobenius elements of the two primes that lie over three, they have ordered nine the Frobenius elements in the Galois group because the characteristic polynomial is the nine cyclotomic polynomial. Similarly, if I look at this polynomial you see it is the seventh cyclotomic polynomial. You see all the coefficients are odd. All the coefficients are odd and that this is the seventh cyclotomic polynomial. So the Frobenius elements of the primes over 11 both have ordered seven. So we see that the image of the Galois group acting on the two torsion points contains elements of order seven and order nine. And now I claim that actually the image of the Galois group is SL2F8. So why is that? Well, the Galois action must commute with the action of the Hacker-Otogra, the Hacker-Otogra, the Hacker-Action-Action-Otogra. And therefore it commutes with t modulo two. But you remember what t is, t is z alpha, where alpha is this. The prime two is inert in this number field. And therefore t modulo two is a field with eight elements. And therefore the action must commute with this F8 action. So it has to commute with F8 and therefore it is contained in GL2F8. On the other hand, the determinant is always one because the determinant is equal to of a Frobenius element is the prime times the character value which is plus or minus one of the quadratic character. So it is always one modulo two. So in fact, the image of the Galois group is in SL2F8. So it is a subgroup of SL2F8. Now SL2F8, we know what the maximal subgroups are. They are either borrel or carton or split carton or non-split carton. But none of these groups, some of these groups contain elements of order seven and some of them contain elements of order nine, but never both. The only group that contains both elements of order seven and elements of order nine is SL2F8 itself. So the image of the Galois group just by looking at these few polynomials is equal to SL2F8. This is a simple group, order 504 and it is an AC group, actually well-known in group theory. It has the property that the centralizer of any non-trivial element is abelian. Okay, now what I will, yeah, what this implies also is that A2 is simple because SL2F8 acts transitively on the 64 points apart from zero and therefore the Galois action is irreducible and that implies that A2 is a simple two group scheme over OF. And remember how the proof went over Q. Over Q, in the Abrashkin Fontaine case, there were only two simple group schemes. There was Zmod2 and MUTU and then I had an argument with those to finish the proof. So now it's different. There is this fancy simple two group scheme and it is not even the only one. There are also a few of order two that is also Zmod2Z and there is MUTU, those you always have over any ring, but there are also two other group schemes of order two. I called them GPI and GPI prime where Pi and Pi prime are factors of two, the prime two splits in Q squared with 97. It is a product of two principle ideals generated by Pi and Pi prime and there are two group schemes of order two and they are sort of mixed. GPI is MUTU locally in Pi, Violet is Zmod2 locally in Pi prime and for GPI prime it is the other way around. So you have these four group schemes of order two and this fancy monster of order 64. And now the theorem is, so it is more complicated than over Q that are now five simple two group schemes. Instead of MUTU and Zmod2 you have all those. Well, still you survive. Once you know this, you can argue in a similar way and prove that there cannot be any abelian varieties with good reduction everywhere except A. And the proof is more or less the same. You look at the two-to-the-end portion points of the abelian variety, arguing as I did in the Fontana-Brushkin case, you prove that the order two group schemes, they cannot sit in an abelian variety because you would have too many torsion points over finite fields, that's impossible. So the group schemes of two-to-the-end torsion points, if you filter them with simple steps, all the simple steps are isomorphic to A2. So with this A2, A2, A2, A2, A2, A2. And now the question is, how can you glue these A2s together and make A2 to the end? And that has to do with the question, how many extensions are there? And there is, of course, one, there is A4. This is an exact sequence. And you prove that it is the only one. That is an argument that I will skip. You prove this is the only one. And once you know that, then it is formal to prove that in fact, you can only get A2 to the end. I mean, the only finite flat group schemes that sit in the abelian variety are isomorphic to A to the two-end. And then you use Falking's isorganic theorem and prove that the abelian variety is isorganic to a power of A. So that I will skip. So the question now is to prove theorem two. To prove that the only simple two-group schemes are those five. Okay. Now remember how we did that in over Q? Remember, we used odlisco. So we're gonna do the same. So we take the simple two-group scheme, we join its points to our fields and we get an extension. And odlisco tells us that there is a bound on the root discriminant. And in this case, the bound is four square root 97. And that is about 39. And then you look in odlisco's tables and then you find a bound on the degree. Remember over Q, the bound on the degree was five. And we could control that.  So that is what happens when you collaborate with Lasina, I guess, when you get these huge bounds. And so it was rather easy over Q to control this field that had degree at most five and is only ramified at two. Now the bound is much larger. And yeah, I think I will skip this. So I want to control the number of fields that are extensions of Q square root 97 and are unramified outside two and have root discriminant at most this. And basically I look at the maximum possible such number field. And you cannot really phrase that in terms of the root discriminant, but in terms of some ramification index, which I will ignore for now. So I look at the maximal extension of the field Q square root 97 for which a certain ramification index satisfies this. And this is in fact, what Abrashkin and Fontaine proved. And it implies that the root discriminant is at most this, but this behaves better. Now what we do is the following. We first compute the maximal solvable sub extension in this field. And this is done with classical theory. And we find that this is a field K prime of, and it has degree eight. Here it is. Now, but we know another subfield of this field K double prime because we have our ability in variety of dimension three. And we know that if we join the two torsion points of that ability in variety to Q square root 97, then we get an extension with Galois group SL2F8. So we join also those points to our field. And then these are disjoint field extensions because this is a solvable extension and the group SL2F8 is simple. And we get this huge extension inside our field. So this is F, the degree eight extension and a degree 504 extension. And now we can estimate what is the degree of the piece that is left. So that is at most, well, half a million divided by this degree. And this is more or less 58. And this is less than 60. And therefore we know that this Galois group is solvable. And then you can prove, once you know this is solvable, you can actually prove, since this is a maximal solvable with a little bit of group theory, you can actually prove that this must be equal. This must be equal. So it means that we actually know the field that we get. It is the composite of the maximal solvable extension of degree eight and our SL2F8 extension. And it follows them. Now, so this is what we know. If I have a simple two group scheme and I join its points to Q squared with 97, then I get this field here, this field. And this field is the composite of a simple, the Galois group is a simple group, SL2F8, times a solvable group of order eight, a two group. Now, if I look at the action on my simple two group scheme, then the solvable, this again is a two group. It must act trivially. So it means that the Galois action is through SL2F8. If I have a simple two group scheme, the Galois group acts through SL2F8. Now, there are two possibilities. Since the group is simple, it either acts trivially or it acts faithfully. And if it acts trivially, then the group must have order two. And well, that takes care of my, where are they, my four group schemes of order two, this one, this one, this one, and this one, or it acts faithfully. And then I claim it must be a two. So, but I have not proved that yet. I only prove that if I have a simple two group scheme that doesn't have order two, then if I join its points to my two fields, I get the same field. And that's not the same. So now what we have to prove in order to prove theorem two, and therefore theorem one, that if I have any simple two group scheme and I join its points to Q squared of 97, I get the same and I get the same extension that necessarily these two group schemes are isomorphic. So that is theorem three, that if I know that the fields are the same, then the group schemes are the same. Okay, well, in order to, let me briefly say how you prove that, because I do not have that much time anymore. So let's study a little bit this extension. So we have this SL2F8 extension. Let's look. So we know this extension is only ramified at two and infinity and it is un-ramified everywhere else. So the local Galois groups are all un-ramified except for two, the two primes over two. And I claim that the local Galois groups are actually Borel subgroups. So they are upper triangular groups of order seven times eight of order 56. And their inertia subgroups are of this form. They are of order eight. And why is that? Well, locally over the, locally the ring is the ring of two-adic integers over both primes over two and over such rings, over such local rings, that is always the local ethyl exact sequence. So your group scheme has a connected component, which is a local group scheme. It has only infinitesimal points and the quotient is an ethyl group scheme. So you always have this. Moreover, in this case, we know that A2 admits action by F8, by it is an F8 vector space scheme and by functoriality the same is then true for the ethyl part and for the connected part. So we always know that. And now I claim that both these parts have order eight. And why is that? Well, you see, if now I look at the characteristic polynomial, the one that I showed you all the way in the beginning, of the primus over two, it looks like this. And if you substitute one, then you count how many points there are rational over A2 and you get 17. So A2 has no rational points over F2. But if I now go to a degree seven extension, then you see it is divisible by eight. So that means that there are, that this ethyl part is not trivial. It has ordered at least eight. And in an abelian variety, it also cannot have more than eight elements. So it has precisely eight elements. And therefore this one also has eight elements. So these are group schemes of order eight. And the Galois group acts on it. Well, it is compatible with F8. So this is a one-dimensional F8 vector space. And the Galois group acts through F8 star, which is a cyclic group of order seven. But Q2, the two added numbers, have no cyclic extensions of degree seven, except the unremifed one by local classroom theory, if you like. So the action on this group is through an unremifed character of order seven. And it's not order one because it didn't have rational points, more the order seven. And since the determinant is one, then the same is through here. So that proves that we have a Borel group. A and D give the action through an unremifed character of order seven. And the B is non-trivial because if the B were trivial, then the action is unremifed on A2. But it is not unremifed. So, yeah, that shows this. Okay, so this I know for A2. For A2, then, yeah, so this is diagonalizable, this is ethyl, and this is diagonalizable by the velati. Now I prove for an arbitrary simple two group scheme that this is also the case. So this is already one step towards the fact that in all simple two group schemes over OF, in some sense, come from this opinion for right. So I claim that over OF, there is always an exact sequence of this type with C ethyl and M diagonalizable. And the consequence of this is, and this will be important in the rest of the proof that I will skip, is that if I take two elements in the inertia group, then you see tau minus the identity kills C. So if I apply tau minus the identity to G, I end up in M. But on M, the action is also unremifed because it is diagonalizable and it is killed by two, then sigma minus the identity kills M. So I have this, I know this relation that sigma minus the identity times tau minus the identity is always zero on the points of an arbitrary simple two group scheme. And this follows essentially from Renault's classification of two group schemes. So in this group scheme business, you know that group schemes are determined by the Galois action if the ramification index of the basering is strictly less than P minus one. And if it is equal to P minus one, you do not know this, but then you know if you look in Renault's paper, that can be at most two group schemes that gives the same Galois module, an etal one and a multiplicative one. And here we are in this situation, P is two and Z two is unremifed, so E is one. And then in fact, there are at most two, there is an etal one and a multiplicative one. And therefore the G zero must be multiplicative and the G, yeah, multiplicative means diagonalizable, sorry. Okay. And then here I then I will stop. So I will then prove that at least the Galois modules of an arbitrary simple two group scheme is equal to the Galois module of the two torsion points of the Abellion variety. And this you can prove as follows. You know that the action on the points of this simple two group scheme is irreducible because it is simple. Moreover, it is killed by two. So you have a representation, irreducible representation of SL2F8 with coefficients in F2. Well, those are classified. This is modular representation theory and in the paper by Brouwer and Nesbitt, you can find what they are and they can have dimension up to 12 or something, six, eight and 12, but only one of them satisfies this property that we have just proved that that's the sigma minus the identity times tau minus the identity is zero for sigma and tau in the two seed of subgroup of this SL2F8. No note that the two seed of subgroup is precisely this group of upper triangular matrices here. So thanks to that property, you can now prove that at least the Galois modules of these two group schemes are isomorphic. Then you also prove that the group schemes are locally isomorphic over the local rings and then a general argument of art in shows that they are in fact isomorphic over the ring itself. And then we are done. Then we have shown that any simple two group scheme over OF that is not of order two is necessarily isomorphic to A2 and that proves theorem three and that proves theorem two and then we have also theorem one. Thank you for your attention.


And here we have some KVM boards and who are you yeah, I'm Moorthy from KVM This is the Okyan TX 83XX board with the 24 cores Yeah, I'm 64 cores It's quite popular right now It's not a server class mode. This is that is different that is called thunder This is Okyan TX, which is kind of embedded platform This is for cellular networks What we have here are 5g emulators Generating traffic for 5g cellular networks, and they're going through a single fact Present the backhaul of the 5g network Because right here you're talking about There's a little Nokia logo there and Talking about 5g emulators Where they are generating the 5g emulators. Which one is a Nokia hardware? So it's a Nokia base station It's just an emulator Yeah, in real world they'll generate they'll have the base station. They'll generate the current one. Yes But it's already in the market or it's not yet? No, not yet. It's a proper concept So and then we have the Okyan TX hardware here. This is from KVM. Yeah, and that's handling the IPsec tunnel Yeah, so it's a single essay capable of doing 18 gigs of profit So What are you doing? What are you showing here? So this is doing ESP tunneling So encryption and authentication of the traffic at line rate, which is it's a 10 gig fat line So we are doing bi-directional traffic now nine gigs this way and nine gigs this way So it's total of 18 gigs. This wire is capable of 20 gigs. We are maxing out the line at this point This is one side of the cellop. That's the other side of the cellop So is it exactly the same exactly the traffic is running in both directions It's a tunnel created between both of these nodes, right? And is this a very important functionality for this to be Yeah, so every phone call you make every data. It's going through this for all 3g 4g 5g And this makes it secure the channel secure It's completely running in the user space. It's completely running in user space. I mean that is the most important thing in the OFP, which Nokia Provided is the complete stack which runs on the user space And open source So this is part of the networking LNG and how far are you with this much more work to be done or So we have done two weeks of work on this so far two weeks so far. That's it. What's next next? Next six months. We want to hit like 80 gigs Till pending a lot more 80 gigs 100 gigs It's all going to come and all the work you're doing here is compatible with the next generation Absolutely. This is a Octane TX2. Exactly. So what we are running is open class, open data plane Specifications we have implemented on our platform No, it doesn't so so every time a cell phone user is connecting or sending data or receiving data You have the RNC, which is sitting in the middle that cell phone tar So this is the backhaul from the cell phone tar talking to the central cellular stations or other cell phone That's your IPC You have some code you can show This is one of the OFP consoles So so you do some pretty good work Yes, absolutely. And the things are moving fast. Very good. Yeah a lot of more interesting things to do Yeah, I mean so this specification is still very new so the more features need to be added You're just scratching the surface in terms of implementation of the IPC More features need to be added a lot more to be done in the next six months We are also getting an extension chipset for this which has more hardware features So all this works on the next generation chipset as well And Yeah The whole thing it's mentioned here what what this can do the chipset can do it is a hardware scheduler Which accelerates the whole load balancing kind of stuff by itself the chipset has the capability


Go over some things and do a little Q&A. I would love to do that and maybe I'll hand out some wrenches. I think Katie's got one coming up. All right, let me see. There's that. I also want to put in the CNBC, CNBC, let's see.  You talk about flair, I'm not gonna buy flair. I'll still hold on to my XRP, I still have some but I'm probably not gonna buy flair. Haven Peck says, be happy with less, my eighth favorite channel. Hey, I'll take it, I'm in the top 10. Ben's chair is here, please, that's good. Cal with a K. Well, Cal, I did tell you, didn't I? That if you keep showing up, if you keep showing up, time for a wrench. Let's see. Gosh, I haven't got a way to wrench in so long, how do I do this? Wait for it, hold on. I guess it is over here. No? Yeah, yeah, yeah. Cal with a K, do me a favor, put in something. Yeah, make a comment so I can put it in here. Thai Boy says, any update with meld? Not yet, not that I can share with you but it is good news. I just, I can't, I can't yet. There's some good things in the rise and I feel, which has finance, the chart, that chart looks awful. They all look awful. Rusty Bot says, it's not 99.5%, yeah. Yeah, and Haven Peck said, yeah, someone paid 650 bucks. Imagine trying to get that money back. No wonder that thing dumped so hard. Wasn't that one of the darlings of scam and white man freed from FTX? I think so, did I miss it? Yeah, retro, we're all feeling pretty bad about the wars but like I said, cooler heads prevail and then it was very interesting to see this Hamas is open for a truce discussion. Imagine bringing someone that, I don't want to comment about it because I don't know enough about it. I'm not a geopolitical expert. Let them figure it out. Okay, Moa, talk about mine. Moa, yours is XRP, unless something else changed. I know it's Bitcoin too. I know, I believe it's polygon as well. I saw Ben put it back, it's so disrespectful. Banks said, did you create that meme yourself? Yes, I did. I thought I did a pretty good job on this one. I thought it was funny. Most people did, some people did not. That was hilarious. And this is really what it is, you know, if I'm talking about your coin, you're like, cool. Very, I think the majority of people don't care if I talk about alts that they don't own but there's some people that, man, if you get out of their wheelhouse, you're the anti-Christ. Yep, Hopium, I gotta admit. Everybody needs a little Hopium. That's what keeps us around. Right, Panda says, I wish I could go to Mozambique to see this, the aerostat. Isn't that cool? That's cool that they did it. But I'm telling you guys, just watch this Netflix first episode. It's about an hour long. A super pump, the battle. There's them bringing Uber into San Francisco first, then New York and then globally and what they had to go through. You think it'd be an easy tech play but they got persecuted by the government just like we're getting persecuted. Well, they got persecuted by state government just like we get persecuted by the federal government. It's the same thing. And of course, the way that they took it to them and showed them how, why it was gonna be successful was a thing of beauty. Now I know it's commercialized and sensationalized but still it was pretty good. Will says, this is worth going on for hundreds of years. It's a flip. I have to agree. Let's start popcorn. I think it's already out there. Yep, aerostyle or play-doh. Except the army is quite global, I know I'm in it. Ah, there's Mollett making friends all over the place. Look at him go. Soul holder, yep. Mike says, Soulon is the only altcoin owner. It's pretty good, Mike.  I will say this, everybody, 75% of my portfolio still is Bitcoin. So 10% is Ethereum and the rest kind of come from there. But I made all my ROI in alts last time. I expect to do it again. We'll see. Yep, ICP. ICP has no max limit. Neither does Ethereum. So I know it's deflationary. Not the last 30 days though. Oh, that's what it was. Crypto max, it says ICP was f-ed over by Solana SPF. Research it. Research, okay. Solana is scared of ICP because it's the real deal. Ooh, we'll see. Yeah. No, it's 5K to 20 people. So 20 people are gonna get 5,000 sweatcoins. Now, a sweatcoin right now is a penny. So it's not, you know, a ton of money that you're gonna be like rolling in it, but let's say it goes with 10 cents. Hey, not too bad for doing just for walking around. And I gotta tell you, the thing I like about, let me show you, the thing I like about sweatcoin are the stories like this, where people write in and said, yeah, I weighed 98 kilos and now I'm 81 kilos thanks to sweat economy. And that's just it, like it motivates you. Like, I'm not gonna get into health and fitness, but it's way easier to stay in shape than get in shape. And sometimes it just all really just comes down to motivation, cause we all know we should like, you know, walk around and not have our belly over our buckle and be able to see our toes and not have a blood sugar of 500 every day, you know, stuff like that. We know it, but it just comes down to motivation. And if you can get there, it's not too tough.  I mean, the app has been around for seven years, 120 million downloads, number one or number five, somewhere around there, top health and fitness app globally. And you can buy stuff with it, so why not? Delboy, drive you any thoughts on Jasmine coin? Nope, I don't own it. So I don't, I know anything about it. I'll tell you what I think I know, what I don't, I don't know anything about Jasmine. Very sorry. Rusty Bot says, cat for the wrench, is cat even here? I'd give her one. Scott says, hey, Ra, I don't need a wrench. Okay, Scott, next one you're here, wrench is yours. I need some more wrenches. Joe Huggs, same thing. Adri says, Ra, do you ever see melt reaching a dollar? I honestly never thought that I'd see the all-time high for Bitcoin back to 20,000 again, and here we are. I never thought that when I was buying Ethereum under a hundred bucks, like 96 or 86 bucks, I never thought it would go back to 1,000 when almost to 5,000. I never thought that Theta would be over five bucks. I was buying it like under a dollar. So nothing's outside the realm of possibility, that's for sure. The question is which one's gonna be, I don't know. But yeah, I can see some things. Scam-winkman, scam-wink-sman fraud. And Vera says it very correctly, peace please. Boy, when cat comes in here again, she'd be like, oh, I could have had it. I'll give it to her next time, everybody remind me. Bot and Tesla and Mollit, oh hey, I must have done it. We did it, everybody. Just by doing this live stream, we single-handedly increased the market. Congratulations. I mean, it was tough, but we did it. Brian Guy says, Rob, he had Tyler Spalding back game on the new Ampera protocol launch as they announced at the beginning of second audit last week, should be wrapping up, sure. Why not? Soul still has SPF stink on, I'm afraid to touch it.  Solana. And if you were dollar-cost averaging Solana in the beginning of the year, you're up. You're up more than you are Bitcoin. Let me make sure that's true. Don't want someone to be like, oh no, no, no, that's not true. Okay, so let's pick the date. 2023, January 1st, to today. Oh, I stand corrected. Solana is up 7.2% and Chainlink is up 8.3% and Bitcoin only 6.7%. So I was right on the Solana, but I was wrong on the Chainlink. I didn't know it did that well this year. Hey, look at that. That's in a cruddy year too. So I know, you know, Sam's stink on things, but we got to move past Sam. He was just the Bernie made off of crypto.  That's just the truth. Crypto golfer, you're right on time, 15th hole. That's true. Anderson Horowitz is an IPC. And as a matter of fact, I must've been looking at something else, but that's not saying much because Anderson Horowitz is in everything, which is, we know that. Pool is cool, it's green screen. It's great as it grew and kind of for use. Give her one, yes. Rob, do you think, do you not think all the fight in the world is the best argument for no CBDCs? If I had to fully show I'm in trouble if cash is CBDC form? I will tell you this. This is why like, I think CBDCs would work out pretty well per country. I mean, kind of, but I mean, here's the thing. If for the exchange rate, you know, we want to do a CBDC and then of course people want to come to America or UK or whatever they want to come in there from China, are you really going to trust the digital you want? I wouldn't. Like, I'm not going to use that, the CBDC version. I'm not going to use the Venezuelan CBDC, it's worthless. I'm not going to use any of that stuff. And I'm pretty sure that China and Russia and parts of the Middle East are not going to want to use the CBDC that is the US dollar so they can get tracked everywhere. I just don't see CBDCs, I mean, within the country, sure, and the people that we trade and have commerce worth, I suppose, but the best thing would be to be some kind of third party that nobody has any kind of stake into and I think we all know what that one is. BitConnect, no, that's not it, don't mention me. Probably Grace's, oh, it's gone. I don't know what happened there, hold on real quick. Sorry about that, that was weird. Okay, oh my God. Iran is hacking the world, I guess so. I don't know what it was, I'll figure. I thought I got de-platformed. I was like, wow, that was fast, it really found me. So let's see, wow, 600 you hung around. Thanks, it's pretty nice. Yeah, no kidding. And another thing, speaking of wallets, did everybody, I don't know what wallets you guys are using, but the tangent wallet just released there, like you can now do mnemonic phrases and the private keys, you can control those now. So if you're looking for another cold storage wall, I think this is the future, honestly. I'll just link in the description. Since 2018, almost a million wallets created, not one has been hacked, just saying. Scott says still ledger, nothing wrong with that, Scott. Ledger, I still have my ledger. Matter of fact, it's right here. I still use it, use it every day. I just, there's some things I don't like about it, but you know, all right. Now my dog's gonna start barking, so this is it. Guys, thanks so much for sticking around. I do appreciate it. If you like today's video, thumbs up and subscribe. But remember, I mean, these things are gonna keep coming at us, and it's gonna be negative. Just deal with things you can control, and the only thing you can really control is your reaction to such events. And that's it for today. So thanks so much, everybody. I'll see you guys in the next one when I give Katie hers wrench. Thanks, everybody. Adios.


from Las Vegas. It's theCUBE, covering AWS re-invent 2018.  We are back in Las Vegas here at AWS re-invent. Along with Rebecca Knight, I'm John Walls, and I know what you're thinking, email. Oh my God, email, the avalanche, the problems that it causes your folks in IT. Well, I tell you what, Chris McFadden is here to solve your problems. VP of Engineering at SparkPost. Chris, good to see you this afternoon. Thanks for joining us. Good to see you, I'm happy to be on theCUBE. Yeah, great. This is my third time in re-invent, but first time on theCUBE, so happy to be here. Oh, so a CUBE rookie. That's right. We have a fine stick to leave you with it on the way out. Remind me to get it to you. All right, so tell us about SparkPost first off, about, we talked about email, I mean what your primary focus is, and just the challenges that you're trying to solve for your clients. Sure, yeah, SparkPost is a leading email delivery provider. So our customers send over five trillion emails a year, that's over 37% of the world's commercial email, so that's obviously a lot of email. So we're focused on a B2C email, and what that means is that any app who has the need to send email, we help with getting that email on time into the inbox. That really helps product managers and product teams with ensuring that they can get the right kind of performance, the analytics, and also the human services to make sure that they can get customers to adopt their service, grow engagement, and ultimately revenues. I understand you have a new product, SparkPost Signals. Tell our viewers a little bit more. Yeah, so I'm very excited to talk about SparkPost Signals. So as everybody knows, email is super important to people. And with email being such a high ROI for most companies, when you have a dip in email performance, that can really impact a company's revenue as well. So I'm excited to talk about SparkPost Signals because what that can really help with is being able to provide some dashboards and tools so that you can have more data-driven, predictive, and actionable insights so that ordinary customers can have that kind of email expertise at their fingertips really to be able to then boost their performance. So I can certainly talk about some of the particular challenges that this would solve for people. So in particular, we have a health score and also spam trap reporting. So for example, what can happen is if you or maybe somebody in your organization that you don't even know about, they could go out and acquire an email list. More email addresses, the better, right? Sure. You know, you end up landing on spam traps. You're getting blocked, your email's not going out. So it's better off to get early notice about whether there's some sort of problem so then you can actually react and correct the problem before it starts impacting your business. So is it a delivery problem or a challenge or is it a firewall challenge or a problem?  Actually, it could be a little bit of both. So email is very much an open network. There's no one particular tech company really owns it. So anybody can send any email, right? That's why most email that's sent is actually spam. So on the ISP side, these are the internet service providers who are like Gmail or Hotmail that are actually receiving the email. They're very protective of their users, right? So what that means is that if you buy email addresses or you're sending too much to people and they say, I don't want this email, then the ISPs can actually say, you're doing this too much, you're being abusive and we're actually going to start blocking you. So none of your email is actually going to get delivered. So none of your password resets, none of your order confirmations, none of your marketing email. So you have to be very, you have to have very good email sending practices otherwise you run into trouble. So for most customers, for most companies we work with, their expertise is elsewhere. They're in social media, they're in banking. Marketing, whatever, right? They don't necessarily know all the best ways to be able to manage their email streams. And yet email is mission critical to their businesses. Exactly. This product launches in January, but you've already been testing the waters a bit with some of your customers. What are you hearing, what are they saying? So we've heard a lot of very good things. The usual response from customers is, when can we get it, you know? So we're frantically working to roll this out, right? But we've actually, when we were doing the demos with customers, we were actually showing them real data so that, so this wasn't hypothetical.  Also showing, which is really interesting, their engagement cohorts. So what that means is that if customers, I mean, if our companies that work with us are not sending to their most engaged users, but are also sending to users that don't actually engage much at all, then that can actually hurt their overall deliverability and engagement. Sure. So when we showed them these cohort reports, showing them that if you actually are sending more to your more engaged users, ultimately your engagement and revenue is going to go up. So we've actually worked, even before Signals was a product, we've worked with customers to do this, and we have some very high profile customers who've actually reduced the volume of email they've sent through us, but their engagement has gone through the roof as well as their revenue. We've also worked with customers, and that's more on the engagement cohort reporting. On the other side, when it comes to the spam trap reporting, we've had customers who've actually run into problems where they inadvertently started emailing to addresses that are on spam traps. Spam traps, if you don't know, are essentially like bogus email addresses that are out there like honeypots. And if you email them, then it tells the spam trap owner that you obviously didn't get a real person to subscribe to this or to opt in. So you're obviously following bad practices and I'll report you to maybe a blacklist which will then prevent all of your email being delivered. So we were able to work with that customer to really identify the rate of spam trap hits that they have and they were able to clean up their own practices based on that and then get back in business and actually have better engagement for what they're doing.  So there's a public cloud play here somewhere. Is this about a customer migration? Are you educating people and bringing them along as well to the public cloud experience? Meaning like, what are you doing here? Right. So we have our cloud service and that's built on AWS. We've been in AWS for over four years now and we love coming here learning about a lot of the new technology. We also have a booth here and we're promoting our own service. What we also have is that we have on-premise products, Momentum and PowerMTA and both of those products are heavily used throughout the industry for sending email. So we have a number of customers who are coming to us and saying we're looking to move to the cloud. So we can either help them move their mail streams to SparkPost, which can be very convenient or if they want to continue to run their own MTAs and some of their own infrastructure, possibly maybe they're a bank or maybe they're just not, it's not the right time for them. Then we're able to look at other options potentially, things like hybrid analytics and that's a way for them to be able to get the additional analytics and things like SparkPost signals but without actually moving everything. But I'm definitely very encouraged. Yesterday's keynote had Guardian and that's quite an ambitious project to be able to move to the cloud. So I'm very excited. We're also, SparkPost is one of their SaaS providers that they chose to use in part of their migration. So rather than continuing to try to run their own infrastructure, they said, here's an API, I trust SparkPost. They've got the right security, the support services and things like that to be able to get the job done. I'm curious about the future and sort of will email always be an integral part of doing business for companies and sort of what, how SparkPost is thinking about its future business model. Right, so email's been dead about 20 years. That's what they keep saying. However, every year, email volumes keep growing. Everybody has an email address. It's the, really there's the preferred method of communication even among millennials nowadays. Email is also, again, it's an open platform so it's not controlled by the big tech companies. And so it's very ubiquitous. It's also a good system of record and also there's certain things that don't really make sense to send over push or SMS. So email continues to be a real workforce for companies both in triggered email as well as marketing email. So we have a number of customers who are in these next generation, MarTech vendors who are providing even more services. They use us as the back end for doing that delivery but they're seeing even more demand for again on the marketing side. And again, there's more and more apps being built. There's more and more opportunities there. They all need to send email. And we see certainly with SparkBusSignals and otherwise that with the smart use of data, it really becomes an even better opportunity to grow those relationships with your customers. Right, so rather than just being a transaction, right, that's an opportunity for a relationship building interaction. A value add. Right. Well, five trillion emails. I think half of them, I think I'm sending half of those these days. So maybe you and I ought to talk. Thanks for the time. It's been a pleasure to have you here on theCUBE. And again, we leave you with a parting gift please by all means. I appreciate it. Chris McFadden joined us here and we'll be back with more from AWS reInvent. We are live on theCUBE from Las Vegas.


Welcome, you're still watching the Breakfast and Plus TV Africa and we will be talking about rail transportation. Indeed, the NRC workers went on strike on Friday over a poor welfare package and of course as at Friday, the strike was called off. But joining us this morning to look at all of the issues and why and what they have discussed with the federal government is the President General of the NRC, Mr. Innocent, a Gigi. Many thanks for joining us on the Breakfast and Plus TV Africa. All right, let's talk about the meeting that was held between the Ministry of Transportation and of course the management of the NRC before this track was eventually suspended. Have all the issues that the NRC, you know, the mandate, have they all been met? Thank you very much. Good morning viewers. I would first of all appreciate Plus TV for the role they played during the industrial action that lasted two days. We sincerely appreciate you and the coverage you have given us. I will start by telling you that actually we held a series of meetings within the period that we have been on strike and the first meeting took place in Abuja between the Union and the board members of Railway. The board chairman and the board members were all with us in Abuja. So after an exhaustive deliberation, we moved to Lagos where the Palm State Ministry of Transport and the MD Railway and other colleagues of theirs were waiting for us for a meeting. So we got back to Lagos on Friday and we held a meeting for over four hours, which of course at the end of it all, we came to an agreement with them. It will interest you to know that the issues at stake were not issues that we'll be taking care of now, now, now, today, today, today. So community has been signed and we have given government time to look into the issues and see how it can be resolved. So we are hopeful that sooner or later our problems will be solved. Why do you say the issues are much and they cannot be resolved in the immediate? Can you run us through some of these issues and what indeed the federal government has asked you to do? How long have they said, you know, the federal government has said that it will take to fix some of these issues. Let us know exactly what the issues really are. Okay. First on the issue was an issue of an enhanced salary structure, which of course we've been agitating for over six years. And last year, in fairness to the Ministry of Transport and the management of Railway, it was included in the budget proposal for 2021. When it got to National Assembly, it was removed. So we started all over again this year. And series of meetings has taken place, even with Salaries and Wages Commission, which of course they came to our organization, did a lot of assessment and they were actually convinced that yes, railway workers need enhanced salary structure because the railway worker collects 26,000 Naira as his take home. And so when they saw all this and seen to the fact that our trains are getting revived and people are patronizing our industry, they now felt that there was need for the review. So documents, we submitted a lot of documents and even held series of meetings too with the Minister of Transport, which he promised he was going to assist. And he took documents also from us and we were not satisfied with the follow-up and up to the time we met with him last week Saturday, not the Saturday that our struggle was to last, but the other Saturday. We were not satisfied because he was yet to take the matter to a level that we were expecting that is involving because we pleaded that if he could take our matter to the President of Nigeria, the President could be of assistance because if he grants express approval, then every other organization like Salaries and Wages Commission, National Assembly and all other processes that needed the follow-up will be taking place within the shortest possible time. So we were disappointed that our matter was not taken anywhere despite the submission of the document six months ago. So that was why we embarked on that strike. So issue of salary enforcement is an issue that has a lot of process that needs to be followed. So it's not a process that can be done within a day or two. So in that regard, they demanded that we should give them a little time. Then also we have on the agenda issue of a review of a standard condition of service because the last time a standard condition of service was reviewed was 1978 and it was implemented in 1983 and which of course by law it's supposed to be reviewed on a five-five-year basis. So automatically that brings us to a level that railway is working without condition of service and so a committee was immediately set up that very day which the union were part of the committee to go into negotiations with the management of railway and see how the standard of condition of service will be reviewed immediately and if that is done by the committee it will require the approval of the managing director then it will move to the board chairman of railway for approver and after he approves it will have to move to the ministry of transport and you can imagine how cumbersome the process is so that is why it cannot be done within a day. So we have to give them little time and which of course we agreed that these processes should be done we should be taken to another level between now and 31st of January so that's why we suspended this strike. Okay so you are saying that the communicator was signed the agreement that was reached between the union and the government is that by January all of this would have been reviewed salary structure would have been reviewed upwards and of course implemented and also have you know standard of living improve or working condition improve for the workers is that what you're saying? Yes that is what we hope. Okay so but this is not the very first time you know the Nigerian government is reaching agreement with different unions I mean ASU and what have you the list is almost endless including the doctors communicates have always been signed do you have faith do you think that the Nigerian government would leave up to his expectation and by January you would not be embarking on another strike? Well it is very very unfortunate that a government of Nigeria to some extent don't meet up their own part of the commitment because actually just like you said it is very obvious that ASU are even women for industrial action because I'm aware they have given three weeks notice to government so it's just because government fell in her own path but this is the first time the Nigerian union of railway workers is going into agreement with government and all into the fact that government is sinking huge amount of money in our industry we believe they wouldn't want to let it go like that they wouldn't want it to be a wasted investment so in that regard we are very very optimistic that something will be done between now and that all right aside from the condition of pay that you've talked about are there any issue as regards you know old allowances in fact it will interest you to know that railway worker is a very very patient worker in the whole of Nigeria because I think the last time we went on strike was over 20 years and it's not as if the union has not been pressing home its demands before government before management and before even the national assembly but to some extent when issues that involve railway workers is concerned most of these authorities take it with laxity and that was where we insisted that we must go on this action so apart from these two other issues we have internal issues we have issues between we have issues like a payment of kilometer allowances we have payment of mileage we have a payment of a lot of allowances like that that are not being paid in our organization but it's just because the standard condition of service is very poor these allowances we are talking about where you begin to calculate it will not be more than 220 nera a per day or per week or so on because of the level of the poorness of the standard condition of service so these are some of the allowances and then we among the issues we rose we had issue of this insurance for workers we are we are into group life assurance and which of course to the best of our knowledge since that group life assurance was introduced in runway nobody has ever benefited no next of kin has ever benefited because it this is money that is being paid to next of kin in the event of the death of their loved ones so we have not been benefited benefiting from it at all so but during the meeting the palm segment minister of transport insisted that runway management should immediately compile list of those that are affected and even the necessary documents that are needed be sent to abuja for onward onward processing to the insurance company so we are hopeful that when they look into it also all these monies will be paid so we have a lot of allowances like that that are not being paid to us why because they claim we are not generating but that was in the past but now we are generating huge amount of money on monthly daily basis when we bought in here when you say the nrc is generating huge amount on the daily basis there has been a lot of infrastructure development ongoing in that particular sector if you went to walk us through how much does the nrc generate on a monthly basis is it enough to cater and to all the entire staff some salary to be candid it will not be enough to cater for the entire staff on salary basis but it will be enough to pay allowances so government is paying salaries but allowances are to be paid some of the allowances are supposed to be paid from the internally generated revenue and all this revenue is generated goes to single treasury account so if um government want to assist us in paying this revenue then they need to to set aside particular amount of money that will come to runway for payment of all these allowances quite okay you know runway is not a revenue generation is not a revenue generating organization but a services rendered organization to the nation so we render services and it is quite not expected that with the level of the trends we have on ground that we should be able to generate revenue that can cater for salaries because if government wants revenue to generate revenue that can pay itself then they need to bring more locomotives they need to bring more coaches they need to bring more wagons they need to bring tankers and they need to impose a law because if you go outside Nigeria you will never see a vehicle a truck carrying goods for a distance like from Lagos to Kani but in Nigeria that is the case so when sanctions are put in place that no truck should carry load for more than 50 or 100 kilometers people will have no option than to travel to that than to transport their goods by rail and that will serve as a source of revenue for the organization so but in Nigeria you see that is what our roads done last month you see a truck carrying heavy goods from here to Lagos from Lagos to Kano from Lagos to to Potakot to all the parts of the nation it's not like that in other countries so if we have efficient runway runway can generate and pay itself because I also remember you know the managing director of the corporation expressing some concerns as well saying you know the the corporation cannot generate enough revenue to sustain itself because they have workers across not just Lagos Ibarra but across the entire country even if you know to some parts of the country it's not very effective but you still have workers who are still there and salaries need to be paid well however we're hoping that you know the government and the agency or the body itself the corporation would be you know thinking outside of the box to ensure that they're generating enough revenue so they can cater for their needs but with this introduction of the e-ticket right now the plan to introduce the e-ticketing you think that that would also help you know increase revenue for the corporation yes I think it will it will assist because it has been tried in Abuja that's what we do in our Abuja Kaduna trend and revenue generation has increased compared to the time that the e-ticketing was not in place so we are very very hopeful that that school increase revenue generation but you see we are talking about revenue generation is is is not just limiting ourselves within this Abuja Kaduna trend or Lagos Ibarra trend or Ibarra Ibarra we have the narrow gauge that cuts across 26 states in Nigeria this narrow gauge has been abandoned by the federal government and as we are talking we have been advising we have been thinking outside the box for them but implementation is what is becoming the issue because we have told them if you would buy a new off locomotive say if government can buy like 300 locomotives for the narrow gauge and coaches and wagons and you can imagine and because we then the narrow gauge starts from Lagos to Kanu up to Unguru in Yubi state it goes to Potakot from Lagos it goes to Meduguri from Potakot it goes to Meduguri from Lagos it goes to Joss it goes to all these 26 states I am talking about so imagine we having enough locomotive and enough coaches and wagons that will be running along this axis we are going to make a lot of money but the standard gauge they are basing their attention on does not cover up to 15 states in the whole nation so but yet that is where we depend on the revenue we are generating for now so if this narrow gauge will be put into efficient use we are going to generate far beyond what we are generating at the moment so that is our position so we wish government will take that option of of of reviving the standard gauge of course the ending revenue was very correct by saying we have workers all over the country that is very true because when you go to all these places that narrow gauge are we still have workers there and they are still being paid salaries though we have some trends like one trend that runs in a week passenger's trend from Lagos to Kanu and then we have pipe trends that runs from Lagos to Zarya then we equally have passenger's trends that runs from Kanu to Unguru and we also have another passenger trends that runs between Aba and Kotako so if they would be sustained and new locals would be put in place to run as it was running in the past I assure you that railway can pay itself all right Mr. Jiji on the final notes now do you think would get to a level very soon in Nigeria where instead of driving you know some distance within interstate and Nigerians would actually believe in the rail system and leave their cars at home and decide to opt for this rail travel anytime soon sorry come again I didn't get you don't I didn't get that do you see us getting to a state where or a state when Nigerians would actually want to leave their cars and would rather want to use the rail services you know in any in any time soon in Nigeria yes yes if I were we're already there because during the the two days one strike I was in Abuja to coordinate the Abuja branch of our union so that the strike would be very very effective there I saw a lot of cars parked in our stations these are parked cars that belongs to passengers who travel to Kaduna on our train with the hope of coming back on Thursday but unfortunately because of the industrial actions they couldn't come back and so their cars were still there up to Friday that I was still in that station so we are there already so but our deal is not yet enough which of course we are still agitating that government should do far more better than what they are doing now so that we get to a level that you don't need to use your car even from your home because if you go to outside country there are different kinds of trends that you will see around you see the tram you will see the the subway you see the bullet train but we don't have any of such trains here yet and all those trains I mentioned are electric trains and yet we are still using diesel trains even this modern train we are talking about is diesel locomotive that we are using we are not using electric gate in Nigeria so until we get there we would have efficient use of our rail system in Nigeria but for now we are close to getting all right thank you for your time indeed we have been speaking with a innocent a gg president general national union of real workers or railway workers and that we have been talking about and the strike or one strike that was just called off on saturday we do appreciate your time thank you very much all right that's the size of the show for today we want to say a very big thank you to all of you who have you know tuned in to watch that of course we talked about the fuel electricity system that is and of course the real workers calling off this track and that's it if you missed out on any part of the conversation it's all right to follow us on our social media platform on facebook and instagram it's at plus tv africa and youtube plus tv africa lifestyle i am messy vocal do you have a great morning and i'm justin katania join us momentarily for the news on the r bye for now


Good day, fellow investors. Caplus S stock analysis is not a stock that I will invest. It's a high risk investment, but it is a perfect example of how low artificial interest rates in Europe are helping zombie companies to survive. So Germany is keeping interest rates low, not only to save Greece or Italy, but also to save itself. Let's see. If I compare global that are competing amongst themselves, fertilizer producers, Caplus S is having no cash flow yield, it has a huge debt, it has management issues, it has EBITDA, but the debt to EBITDA is 7, so it's completely different from other good companies like CF, like Nutrien. The Moisaikis somewhere in between and Yara is again highly stretched for their promises. What's going on with Caplus S? They have this strategy that they have implemented up to 2030. Have you ever heard the management implementing a strategy up to 2030? However, they have to do that because they need to borrow money just to survive. They hope to reach positive cash flows after the big mistakes of the past, some weather influence okay, but still the positive free cash flow will be hard to achieve if they miss on their promises. Their promises are that they will grow over the next, in this case, 15 years at 9% per year, even if the fertilizer market grows at what, 1.5 to 3% per year on average 2%. More they're going to grow 9% when they were terrible in the past beats me, but this is the promise they are promising their bondholders just to get the money and the bondholders are desperate to get some yield. And things are not going well. They have had productions, standstills in Germany, the Bethu in mind that they invested huge amounts of money is challenging because product quality, it's not ramped up yet. So big delays, bit costs, the EBITDA is 600 million euros, but still with the huge debt of 5 billion and the investments and the CapEx hard to achieve cash flows and they still, even with debt to EBITDA of 7, they still pay dividends. This is the worst reason to pay a dividend. This is intended to express our confidence for the current year.  But people love the dividends and they are willing to sustain. The fact that this is alive means that there is so much money in Europe that doesn't know where to go and fulfills the wishes of such a zombie company. As I said, they have 4.5 billion euros in debt. The debt to EBITDA is huge at 7, which is something crazy. The Bethu in mind will be completed only in 2023 and their target is to have lower cost one-third lower than their German plans. Cash unit costs 200 euros per ton, that's $260 per ton. Mosaic, Nutrient, their targeting costs lower than $100 per ton. So even if Betune is 40% lower than this, it will be even more expensive than Mosaic. Nutrients that can just turn on again a mine like Betune at no cost practically. Plus the Russians, White Russians, Belarus is much, much cheaper. The only thing keeping Kepler's assets alive are the European interest rates. So I would call this a zombie company. So this company with terrible debt levels, terrible management, terrible success based on just one promise can borrow money up to 2024 at 3%. 3%. Nutrient, the leader in the potash industry that can destroy this company, but just putting 5 million more tons of production that they have idled at very low cost. They are borrowing at 4.5%, 5%. So it's crazy how this thing is alive, but they can take tank the ECB. Turnarounds are always possible, but 9% growth per year over 15 years. Who are you? Bill Gates and Microsoft. So it's really crazy and of course pension funds, they look at the yield 3%. Yes, I know it's European junk, but I have so much money, I have to be diversified. Let's buy them and the ECB knows that and that's why the ECB will not increase interest rates because these guys would go bankrupt as would many, many other companies in Europe. So this is the situation. Unfortunately, this is not healthy because they have the money. They put up unprofitable businesses and the real businesses that really focus on lowering costs like Nutrient are again hit because it's not fair, the markets are rigged and it's not fair for let's say healthy competition. Sooner or later, this will have to end because even with low interest rates, these guys are not able to turn a profit. If they grow 9% per year over the next 15 years, the EBITDA might get revalued, go from 600 million to, I don't know, 3 billion, which is their target. Times 10, it's a 30 billion company. Current market cap is a 3 billion company, but it's impossible that they grow at that rate. They will grow at max, at best, at 3% per year. So they will go to 900 million in EBITDA over the next 10 years. Given the debt, they will be forced to sell their assets at minimal prices. Even the bondholders should lose their money. So really, really a bad situation, but kept alive by the situation in Europe. So Germany is saving also itself because there are lots of zombie companies in Europe and low interest rates are the only saviour. Thank you for watching, looking forward to your comments on this one and I'll see you in the next video.