𝑝-adic periods and derived de Rham cohomology

Beilinson, A.

doi:10.1090/S0894-0347-2012-00729-2

$p$-adic periods and derived de Rham cohomology
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by A. Beilinson

J. Amer. Math. Soc. 25 (2012), 715-738

DOI: https://doi.org/10.1090/S0894-0347-2012-00729-2

Published electronically: January 27, 2012

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Abstract:

We show that derived de Rham cohomology of Illusie satisfies the $p$-adic Poincaré lemma in h-topology. This yields a new construction of the $p$-adic period map and a simple proof of Fontaine’s C$_{\text {dR}}$ conjecture.

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