Integral $p$-adic étale cohomology of Drinfeld symmetric spaces

Abstract

We compute the integral $p$-adic étale cohomology of Drinfeld symmetric spaces of any dimension. This refines the computation of the rational $p$-adic étale cohomology from Colmez-Dospinescu-Nizioł. 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 Česnavičius-Koshikawa which replace the quasi-integral comparison theorem of Tsuji used in CDN.

References in corpus (2)

• On special representations of $p$-adic reductive groups
• $p$-adic vanishing cycles as Frobenius-fixed points

Cited by in corpus (1)

• On uniqueness of $p$-adic period morphisms, II