Finiteness and duality of cohomology of $(\varphi,\Gamma)$-modules and the 6-functor formalism of locally analytic representations

Yutaro Mikami

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arXiv · 2504.01780

Finiteness and duality of cohomology of $(\varphi,\Gamma)$-modules and the 6-functor formalism of locally analytic representations

Yutaro Mikami

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Abstract

Finiteness and duality of cohomology of families of $(\varphi,\Gamma)$-modules were proved by Kedlaya-Pottharst-Xiao. In this paper, we study solid locally analytic representations introduced by Rodrigues Jacinto-Rodr\'iguez Camargo in terms of analytic stacks and 6-functor formalisms, which are developed by Clausen-Scholze, Heyer-Mann, respectively. By using this, we provide a generalization of the result of Kedlaya-Pottharst-Xiao, giving a new proof for cases already proved there.

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Yutaro Mikami. 2025-04-02. Finiteness and duality of cohomology of $(\varphi,\Gamma)$-modules and the 6-functor formalism of locally analytic representations. https://arxiv.org/abs/2504.01780

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