Character formula for Weil representations in terms of Frobenius traces
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arXiv
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| Auteurs principaux: | , |
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| Format: | Preprint |
| Publié: |
2022
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| _version_ | 1866908757487779840 |
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| author | Dokchitser, Tim Dokchitser, Vladimir |
| author_facet | Dokchitser, Tim Dokchitser, Vladimir |
| contents | It is known that the etale cohomology of a potentially good abelian variety over a local field K is determined by its Euler factors over the extensions of K. We extend this to all abelian varieties, show that it is enough to take extensions where A is semistable, and give a uniform version over p-adic fields where the extensions are the same for all abelian varieties of a given dimension. The results are explicit, and apply to a wide class of Weil-Deligne representations. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2201_04094 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | Character formula for Weil representations in terms of Frobenius traces Dokchitser, Tim Dokchitser, Vladimir Number Theory Algebraic Geometry 11F80, 11G10, 11G20, 11G25, 14F20 It is known that the etale cohomology of a potentially good abelian variety over a local field K is determined by its Euler factors over the extensions of K. We extend this to all abelian varieties, show that it is enough to take extensions where A is semistable, and give a uniform version over p-adic fields where the extensions are the same for all abelian varieties of a given dimension. The results are explicit, and apply to a wide class of Weil-Deligne representations. |
| title | Character formula for Weil representations in terms of Frobenius traces |
| topic | Number Theory Algebraic Geometry 11F80, 11G10, 11G20, 11G25, 14F20 |
| url | https://arxiv.org/abs/2201.04094 |