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

Piotr Achinger; Sally Gilles; Wies{\l}awa Nizio{\l}

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

Not yet reviewed by Pith; the record is open.

Re-run · record.json Download PDF Read on arXiv ↗

This paper has not been read by Pith yet. Machine review is queued; the pith claim, tier, and objections will appear here once it completes.

SPECIMEN: schema-true, not a live event

T0 review · schema-true

One-sentence machine reading of the paper's core claim.

pith:XXXXXXXX · record.json · timestamp

arxiv 2501.13651 v1 pith:WDEVXG7E submitted 2025-01-23 math.AG math.NT

Piotr Achinger , Sally Gilles , Wies{l}awa Nizio{l} This is my paper · ORCID

classification math.AGmath.NT

keywords compactlysupportedcohomologyadicanalyticetalepro-varieties

verification ladder T0 review T1 audit T2 compute T3 formal

0 comments

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.

Discussion (0). Continue with ORCID to comment.

Forward citations

Cited by 1 Pith paper

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score. Full citation record

Topological Vector Spaces
math.AG 2025-09 conditional novelty 6.0 of 10

A condensed version of the Topological Vector Spaces category is introduced, and fully faithful embeddings from algebraic p-adic vector spaces and from perfect complexes on the Fargues–Fontaine curve are proven.

Pith tools