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

2005/11/28 by D. Kaledin, Kaledin, D.
Mathematics · #Algebraic Geometry (math.AG) #FOS: Mathematics #K-Theory and Homology (math.KT) #math.AG #math.KT

paper · pdf · doi:10.48550/arxiv.math/0511665

53 pages, LaTeX2e

arxiv created 2005/11/28 · arxiv updated 2009/12/01

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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• Non-commutative Hodge structures: Towards matching categorical and geometric examples