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On endomorphisms of the de Rham cohomology functor

Shizhang Li and Shubhodip Mondal

Geometry & Topology 28 (2024) 759–802
Abstract

We compute the moduli of endomorphisms of the de Rham and crystalline cohomology functors, viewed as a cohomology theory on smooth schemes over truncated Witt vectors. As applications of our result, we deduce Drinfeld’s refinement of the classical Deligne–Illusie decomposition result for de Rham cohomology of varieties in characteristic p > 0 that are liftable to W2, and prove further functorial improvements.

Keywords
crystalline cohomology, de Rham cohomology, Deligne–Illusie decomposition, stacks
Mathematical Subject Classification
Primary: 14F30, 14F40
Secondary: 14D23
References
Publication
Received: 26 October 2021
Revised: 20 April 2022
Accepted: 22 July 2022
Published: 13 March 2024
Proposed: Marc Levine
Seconded: Dan Abramovich, Mark Gross
Authors
Shizhang Li
Morningside Center of Mathematics and Hua Loo-Keng Key Laboratory of Mathematics
Chinese Academy of Sciences
Beijing
China
Shubhodip Mondal
Department of Mathematics
University of British Columbia
Vancouver, BC
Canada

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