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On the $p$-adic pro-\'etale cohomology of Drinfeld symmetric spaces
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abstract
Via the relative fundamental exact sequence of $p$-adic Hodge theory, we determine the geometric $p$-adic pro-\'etale cohomology of the Drinfeld symmetric spaces defined over a $p$-adic field, thus giving an alternative proof of a theorem of Colmez-Dospinescu-Niziol. Along the way, we describe, in terms of differential forms, the geometric pro-\'etale cohomology of the positive de Rham period sheaf on any connected, paracompact, smooth rigid-analytic variety over a $p$-adic field, and we do it with coefficients. A key new ingredient is the condensed mathematics recently developed by Clausen-Scholze.
Forward citations
Cited by 10 Pith papers
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