On endomorphisms of the de Rham cohomology functor

Li, Shizhang¹ ; Mondal, Shubhodip²

¹ Morningside Center of Mathematics and Hua Loo-Keng Key Laboratory of Mathematics, Chinese Academy of Sciences, Beijing, China
² Department of Mathematics, University of British Columbia, Vancouver, BC, Canada

Geometry & topology, Tome 28 (2024) no. 2, pp. 759-802.

Résumé

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 $W_2$, and prove further functorial improvements.

Détail

DOI : 10.2140/gt.2024.28.759

Keywords: crystalline cohomology, de Rham cohomology, Deligne–Illusie decomposition, stacks

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