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arXiv · 1601.00637

Spectral sequences for cyclic homology

D. Kaledin
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Abstract

We prove that for a homologically smooth and proper DG algebra over a field of characteristic 0, the Hodge-to-de Rham spectral sequence degenerates. This has been conjectured by M. Kontsevich and Y. Soibelman arXiv:math/0606241 and proved in arXiv:math/0611623 under a technical assumption. In this paper, the assumption is removed, and the argument is considerably simplified (in particular, it no longer uses Dold-Kan equivalence and simplicial methods). We also analyse the degeneration of the conjugate spectral sequence in positive caracteristic constructed in arXiv:1509.08784.

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D. Kaledin. 2016-01-04. Spectral sequences for cyclic homology. https://arxiv.org/abs/1601.00637

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