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Non-commutative Cartier operator and Hodge-to-de Rham degeneration

D. Kaledin
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Abstract

We introduce a version of the Cartier isomorphism for de Rham cohomology valid for associative, not necessarily commutative algebras over a field of positive characteristic. Using this, we imitate the well-known argument of P. Deligne and L. Iluusie and prove, in some cases, a conjecture of M. Kontsevich which claims that the Hodge-to-de Rham, a.k.a. Hochschild-to-cyclic spectral sequence degenerates.

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D. Kaledin. 2005-11-28. Non-commutative Cartier operator and Hodge-to-de Rham degeneration. https://arxiv.org/abs/math/0511665

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