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On the $p$-adic pro-\'etale cohomology of Drinfeld symmetric spaces

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arxiv 2110.10683 v2 pith:7HP42HCL submitted 2021-10-20 math.NT math.AGmath.RT

classification math.NTmath.AGmath.RT
keywords adiccohomologyetalepro-drinfeldfieldgeometricspaces
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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.

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Cited by 6 Pith papers

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