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arXiv · 2501.13651

Compactly supported $p$-adic pro-\'etale cohomology of analytic varieties

Piotr Achinger·Sally Gilles·Wiesława Nizioł
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Abstract

We study properties of compactly supported $p$-adic pro-\'etale cohomology of smooth partially proper rigid analytic varieties. In particular, we prove a comparison theorem, in a stable range, with compactly supported syntomic cohomology, which is built from compactly supported Hyodo-Kato and ${\mathcal B}^+_{\rm dr}$-cohomologies. We derive from that a (limited version of a) fundamental diagram.

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Piotr Achinger, Sally Gilles, Wiesława Nizioł. 2025-01-23. Compactly supported $p$-adic pro-\'etale cohomology of analytic varieties. https://arxiv.org/abs/2501.13651

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