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| Autore principale: | |
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| Natura: | Preprint |
| Pubblicazione: |
2024
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| Soggetti: | |
| Accesso online: | https://arxiv.org/abs/2410.09483 |
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| _version_ | 1866909817059147776 |
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| author | Marquis, Nataniel |
| author_facet | Marquis, Nataniel |
| contents | Functors involved in Fontaine equivalences decompose as extension of scalars and taking of invariants between full subcategories of modules over a topological ring equipped with semi-linear continuous action of a topological monoid. We give a general framework for these categories and the functors between them. We define the categories of étale projective $\mathcal{S}$-modules over $R$ to englobe categories that will correspond by Fontaine-type equivalences to finite free representations of a group. We study their preservation by base change, taking of invariants by a normal submonoid of $\mathcal{S}$ and coinduction to a bigger monoid. We define and study categories corresponding to finite type continuous representations over $\mathbb{Z}_p$ through the notions of finite projective $(r,μ)$-dévissage and of topological étale $\mathcal{S}$-modules over $R$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2410_09483 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Study of various categories gravitating around $(φ,Γ)$-modules Marquis, Nataniel Number Theory Functors involved in Fontaine equivalences decompose as extension of scalars and taking of invariants between full subcategories of modules over a topological ring equipped with semi-linear continuous action of a topological monoid. We give a general framework for these categories and the functors between them. We define the categories of étale projective $\mathcal{S}$-modules over $R$ to englobe categories that will correspond by Fontaine-type equivalences to finite free representations of a group. We study their preservation by base change, taking of invariants by a normal submonoid of $\mathcal{S}$ and coinduction to a bigger monoid. We define and study categories corresponding to finite type continuous representations over $\mathbb{Z}_p$ through the notions of finite projective $(r,μ)$-dévissage and of topological étale $\mathcal{S}$-modules over $R$. |
| title | Study of various categories gravitating around $(φ,Γ)$-modules |
| topic | Number Theory |
| url | https://arxiv.org/abs/2410.09483 |