On the Smooth Part Functor

2021/08/11 by Claudius Heyer, Heyer, Claudius
Mathematics · #11E95 #12G05 #20G99 #Advanced Algebra and Geometry #Algebraic Geometry and Number Theory #FOS: Mathematics #Geometric and Algebraic Topology #Number Theory (math.NT) #Representation Theory (math.RT) #math.NT #math.RT #msc:11E95 #msc:12G05 #msc:20G99

paper · pdf · doi:10.48550/arxiv.2108.05262

4 pages. Comments welcome!

arxiv created 2021/08/11 · openalex publication_date 2021/08/11 · arxiv updated 2021/08/12 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Let G be a compact p-adic analytic group and k a field positive characteristic. We prove that for every smooth representation of G on a k-vector space V, every 1-cocycle G→ V is continuous. We deduce that the first derived functor of the smooth part functor vanishes on smooth representations. As a corollary, we obtain that extensions of smooth representations are automatically smooth.

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