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| Format: | Preprint |
| Publié: |
2024
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| Sujets: | |
| Accès en ligne: | https://arxiv.org/abs/2410.08933 |
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| _version_ | 1866908791798235136 |
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| author | Tang, Jiacheng |
| author_facet | Tang, Jiacheng |
| contents | Solid abelian groups, as introduced by Dustin Clausen and Peter Scholze, form a subcategory of all condensed abelian groups satisfying some ''completeness'' conditions and having favourable categorical properties. Given a profinite ring $R$, there is an associated condensed ring $\underline{R}$ which is solid. We show that the natural embedding of profinite $R$-modules into solid $\underline{R}$-modules preserves $\mathrm{Ext}$ and tensor products, as well as the fact that profinite rings are analytic. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2410_08933 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Profinite and Solid Cohomology Tang, Jiacheng Category Theory Rings and Algebras 18G15, 18B25, 16W80 Solid abelian groups, as introduced by Dustin Clausen and Peter Scholze, form a subcategory of all condensed abelian groups satisfying some ''completeness'' conditions and having favourable categorical properties. Given a profinite ring $R$, there is an associated condensed ring $\underline{R}$ which is solid. We show that the natural embedding of profinite $R$-modules into solid $\underline{R}$-modules preserves $\mathrm{Ext}$ and tensor products, as well as the fact that profinite rings are analytic. |
| title | Profinite and Solid Cohomology |
| topic | Category Theory Rings and Algebras 18G15, 18B25, 16W80 |
| url | https://arxiv.org/abs/2410.08933 |