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arXiv · 2108.05262

On the Smooth Part Functor

Claudius Heyer
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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 $G\to V$ 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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Claudius Heyer. 2021-08-11. On the Smooth Part Functor. https://arxiv.org/abs/2108.05262

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