Take the 2-minute tour ×  I'm sure the following statement is
well-known to experts: Let $A$ be a dga. Let $perf(A)$ be the
dg-category of perfect dg-modules over A. Then there is a quasi-
isomorphism $$C_\bullet(perf(A)) \to C_\bullet(A)$$ between
their Hochschild chain-complexes.  Does anyone know a reference
for it?  I'm aware of Keller's 2003 paper that I think gives the
result for Hochschild cochain-complexes, but I need the chain
version. Thanks!  share|improve this question I tried a brief
look into the literature I know and only found the version for
projective modules (McCarthy's "The cyclic homology of an exact
category", Prop 2.4.3) - and if I delve any deeper I'd likely
end up with a result proved for THH rather than HH which would
require you to translate it. –  Tyler Lawson Sep 23 '10 at 13:27
Shklyarov, in Thm. 2.6 of his paper arxiv.org/abs/0710.1937
quotes a result saying that the natural map, which goes in the
opposite direction of the one listed above, is a quasi-
isomorphism. He references K