DOI: 10.1017/nmj.2026.10138 ISSN: 0027-7630

Compactly supported p -adic pro-étale cohomology of analytic varieties

Piotr Achinger, Sally Gilles, Wiesława Nizioł
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Abstract

We study properties of compactly supported p -adic pro-étale 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

B dR + $\mathbf {B}^+_{\mathrm {dR} }$ bold upper B Subscript d upper R Superscript plus
-cohomologies. We derive from that a (limited version of a) fundamental diagram. This article should be thought of as a compactly supported counterpart of the series (Colmez and Nizioł, 2020, Münster J. Math. 13, 445–507; Colmez and Nizioł, 2025, J. Algebraic Geom. 34, 1–108; and Colmez and Nizioł, 2025, Duke Math. J. 174, 2203–2301) but, in particular, as a continuation of Colmez and Nizioł (2025).

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