2021
DOI: 10.48550/arxiv.2110.10683
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On the $p$-adic pro-étale cohomology of Drinfeld symmetric spaces

Abstract: Via the relative fundamental exact sequence of p-adic Hodge theory, we determine the geometric p-adic pro-étale cohomology of the Drinfeld symmetric spaces defined over a p-adic field, thus giving an alternative proof of a theorem of Colmez-Dospinescu-Nizio l. Along the way, we describe, in terms of differential forms, the geometric pro-étale 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 ne… Show more

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Cited by 3 publications
(7 citation statements)
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“…all metrizable ones. The main notions of the theory of condensed non-archimedean functional analysis we use are due to Clausen and Scholze [CS19], [CS], [Bos21]. All the vector spaces considered in this text are solid K-vector spaces, unless otherwise specified.…”
Section: Statement Of the Main Resultsmentioning
confidence: 99%
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“…all metrizable ones. The main notions of the theory of condensed non-archimedean functional analysis we use are due to Clausen and Scholze [CS19], [CS], [Bos21]. All the vector spaces considered in this text are solid K-vector spaces, unless otherwise specified.…”
Section: Statement Of the Main Resultsmentioning
confidence: 99%
“…In §3 we develop the theory of solid K-vector spaces following the appendix of [Bos21]. Most of the results exposed in this section will be presented in the forthcoming work of Clausen and Scholze [CS].…”
Section: Statement Of the Main Resultsmentioning
confidence: 99%
See 1 more Smart Citation
“…all metrizable ones. The main notions of the theory of condensed non-archimedean functional analysis we use are due to Clausen and Scholze [CS19], [CS], [Bos21]. All the vector spaces considered in this text are solid K-vector spaces, unless otherwise specified.…”
Section: Statement Of the Main Resultsmentioning
confidence: 99%
“…We will use the condensed mathematics developed by Clausen-Scholze. Our references are the lecture notes [Sch19] by Scholze and the recent preprint [Bos21] by Bosco.…”
Section: Galois Invariantmentioning
confidence: 99%