Finiteness and duality of cohomology of $(φ,Γ)$-modules and the 6-functor formalism of locally analytic representations
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arXiv
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| Format: | Preprint |
| Veröffentlicht: |
2025
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| _version_ | 1866912856252874752 |
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| author | Mikami, Yutaro |
| author_facet | Mikami, Yutaro |
| contents | Finiteness and duality of cohomology of families of $(φ,Γ)$-modules were proved by Kedlaya-Pottharst-Xiao. In this paper, we study solid locally analytic representations introduced by Rodrigues Jacinto-Rodríguez 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2504_01780 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Finiteness and duality of cohomology of $(φ,Γ)$-modules and the 6-functor formalism of locally analytic representations Mikami, Yutaro Number Theory Algebraic Geometry Finiteness and duality of cohomology of families of $(φ,Γ)$-modules were proved by Kedlaya-Pottharst-Xiao. In this paper, we study solid locally analytic representations introduced by Rodrigues Jacinto-Rodríguez 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. |
| title | Finiteness and duality of cohomology of $(φ,Γ)$-modules and the 6-functor formalism of locally analytic representations |
| topic | Number Theory Algebraic Geometry |
| url | https://arxiv.org/abs/2504.01780 |