Non-commutative Hodge-to-de Rham degeneration via the method of Deligne-Illusie
By Dmitry Kaledin. 2006
86 citations recorded by the source corpus.
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.
Subfields: Algebra and Number Theory, Geometry and Topology, Mathematical Physics
View Paper: https://www.semanticscholar.org/paper/918a52f00f4fc30ca6c9784f176bc414c17850e3
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In Algebra and Number Theory
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Citations in the corpus
- The integral Hodge conjecture for two-dimensional Calabi–Yau categories (2020, background): “The noncommutative Hodge-to-de Rham spectral sequence and its degeneration [45, 46, 68] gives a canonical filtration of HPn(C) whose p-th graded piece is HHn+2p(C).”
- Topological K-theory of complex noncommutative spaces (2012, background): “the rational structure. The famous degeneration conjecture ([22, 2.2.4]) furnishes a sufficient condition for the existence of a natural De Rham data ; it has been proved in some particular cases (see [19], [32], [9]) and is supported by the existence of a natural connection on periodic cyclic homolo”