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arXiv · 1905.11495

Integral $p$-adic \'etale cohomology of Drinfeld symmetric spaces

Pierre Colmez·Gabriel Dospinescu·Wiesława Nizioł
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Abstract

We compute the integral $p$-adic \'etale cohomology of Drinfeld symmetric spaces of any dimension. This refines the computation of the rational $p$-adic \'etale cohomology from Colmez-Dospinescu-Nizio{\l}. The main tools are: the computation of the integral de Rham cohomology from CDN and the integral $p$-adic comparison theorems of Bhatt-Morrow-Scholze and \v{C}esnavi\v{c}ius-Koshikawa which replace the quasi-integral comparison theorem of Tsuji used in CDN.

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Pierre Colmez, Gabriel Dospinescu, Wiesława Nizioł. 2019-05-27. Integral $p$-adic \'etale cohomology of Drinfeld symmetric spaces. https://doi.org/10.1215/00127094-2020-0084

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