Cup product of inhomogeneous Tate cochains, and application to tori over local fields that split over cyclic extensions
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arXiv
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| Format: | Preprint |
| Publié: |
2025
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| _version_ | 1866911390940266496 |
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| author | Borovoi, Mikhail |
| author_facet | Borovoi, Mikhail |
| contents | In this note we give formulas for cup product in Tate cohomology in terms of inhomogeneous cochains. Using one of these formulas, for a torus T defined over a non-archimedean local field K and splitting over a cyclic extension of K, we compute explicit cocycles representing all cohomology classes in H^1(K,T). |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2508_07288 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Cup product of inhomogeneous Tate cochains, and application to tori over local fields that split over cyclic extensions Borovoi, Mikhail Number Theory Group Theory Representation Theory 11E72, 11R37, 11S, 20G10, 20G25, 20J06 In this note we give formulas for cup product in Tate cohomology in terms of inhomogeneous cochains. Using one of these formulas, for a torus T defined over a non-archimedean local field K and splitting over a cyclic extension of K, we compute explicit cocycles representing all cohomology classes in H^1(K,T). |
| title | Cup product of inhomogeneous Tate cochains, and application to tori over local fields that split over cyclic extensions |
| topic | Number Theory Group Theory Representation Theory 11E72, 11R37, 11S, 20G10, 20G25, 20J06 |
| url | https://arxiv.org/abs/2508.07288 |