Non-commutative Hodge-to-de Rham degeneration via the method of Deligne-Illusie

Details Non-commutative Hodge-to-de Rham degeneration via the method of Deligne-Illusie Non-commutative Hodge-to-de Rham degeneration via the method of Deligne-Illusie

2006-11-21

arxiv.org/abs/math/0611623v4

Mathematics

K-Theory and Homology

Final version, to appear in F.Bogomolov's 60th anniversary volume of Pure and Applied Mathematics Quaterly. Very minor changes

Scientific paper

We use a version of the method of Deligne-Illusie to prove that the Hodge-to-de Rham, a.k.a. Hochschild-to-cyclic spectral sequence degenerates for a large class of associative, not necessariyl commutative DG algebras. This proves, under some assumption, a conjecture by Kontsevich and Soibelman made in math.RA/0606241. The approach is similar to my earlier paper math.AG/0511665, but the proof is more straightforward, and the underlying algebraic topology notions are explicitly described. The paper is independent of math.AG/0511665 and in a sense, supercedes it.

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