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

@inproceedings{Bosco2021OnT, title={On the \$p\$-adic pro-\'etale cohomology of Drinfeld symmetric spaces}, author={Guido Bosco}, year={2021} }

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…

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