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arXiv · 2109.04303

On endomorphisms of the de Rham cohomology functor

Shizhang Li·Shubhodip Mondal
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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 $W_2$, and prove further functorial improvements.

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Shizhang Li, Shubhodip Mondal. 2021-09-09. On endomorphisms of the de Rham cohomology functor. https://doi.org/10.2140/gt.2024.28.759

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