Duality for condensed cohomology of the Weil group of a p-adic field
Fuente:
arXiv
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| Natura: | Preprint |
| Pubblicazione: |
2024
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| _version_ | 1866915202277048320 |
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| author | Artusa, Marco |
| author_facet | Artusa, Marco |
| contents | We use the theory of Condensed Mathematics to build a condensed cohomology theory for the Weil group of a $p$-adic field. The cohomology groups are proved to be locally compact abelian groups of finite ranks in some special cases. This allows us to enlarge the local Tate Duality to a more general category of non-necessarily discrete coefficients, where it takes the form of a Pontryagin duality between locally compact abelian groups. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2402_05565 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Duality for condensed cohomology of the Weil group of a p-adic field Artusa, Marco Number Theory We use the theory of Condensed Mathematics to build a condensed cohomology theory for the Weil group of a $p$-adic field. The cohomology groups are proved to be locally compact abelian groups of finite ranks in some special cases. This allows us to enlarge the local Tate Duality to a more general category of non-necessarily discrete coefficients, where it takes the form of a Pontryagin duality between locally compact abelian groups. |
| title | Duality for condensed cohomology of the Weil group of a p-adic field |
| topic | Number Theory |
| url | https://arxiv.org/abs/2402.05565 |