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

Wieslawa Niziol (1) , Pierre Colmez (2) , Gabriel Dospinescu (3)

1 UMPA-ENSL - Unité de Mathématiques Pures et Appliquées
2 CMLS - Centre de Mathématiques Laurent Schwartz
3 CNRS - Centre National de la Recherche Scientifique

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.

Domaines: Théorie des nombres [math.NT]; Géométrie algébrique [math.AG]

Wieslawa Niziol, Pierre Colmez, Gabriel Dospinescu. Integral $p$-adic \'etale cohomology of Drinfeld symmetric spaces. Duke Mathematical Journal, 2021. ⟨hal-02387669⟩