A note on the cohomology of p-adic analytic group actions

2023/06/09 by Annie Carter, Carter, Annie, Kiran S. Kedlaya +1
Mathematics · #Advanced Algebra and Geometry #Algebraic Geometry and Number Theory #FOS: Mathematics #Geometry and complex manifolds #Group Theory (math.GR) #Number Theory (math.NT)

paper · pdf · doi:10.48550/arxiv.2306.05826

openalex publication_date 2023/06/09 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We prove that given an analytic action of a compact p-adic Lie group on a Banach space over a field of positive characteristic, one can detect either the simultaneous vanishing or the simultaneous finite-dimensionality of all of the continuous cohomology groups from the corresponding statement for the restriction to a pro-p procyclic subgroup. We also formulate a conjecture generalizing this result, in which the base field is allowed to have mixed characteristic and the subgroup is allowed to be nilpotent. Finally, we formulate an analogous conjecture about Lie algebra cohomology and relate this to a theorem of Kostant.

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