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

TL;DR

This paper computes the integral p-adic étale cohomology of Drinfeld symmetric spaces, refining previous rational cohomology results by employing advanced integral comparison theorems and de Rham cohomology calculations.

Contribution

It extends the understanding of p-adic étale cohomology for Drinfeld spaces by providing integral computations using modern comparison theorems, improving upon prior rational results.

Findings

Computed integral p-adic étale cohomology for all dimensions of Drinfeld spaces.

Refined previous rational cohomology results with integral data.

Utilized advanced integral p-adic comparison theorems to achieve these results.

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.