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Mathematics > Number Theory

arXiv:2201.04094 (math)
[Submitted on 11 Jan 2022 (v1), last revised 19 Mar 2024 (this version, v3)]

Title:Character formula for Weil representations in terms of Frobenius traces

Authors:Tim Dokchitser, Vladimir Dokchitser
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Abstract: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.
Comments: 8 pages, final accepted version
Subjects: Number Theory (math.NT); Algebraic Geometry (math.AG)
MSC classes: 11F80, 11G10, 11G20, 11G25, 14F20
Cite as: arXiv:2201.04094 [math.NT]
  (or arXiv:2201.04094v3 [math.NT] for this version)
  https://doi.org/10.48550/arXiv.2201.04094

Submission history

From: Tim Dokchitser [view email]
[v1] Tue, 11 Jan 2022 17:42:02 UTC (16 KB)
[v2] Thu, 17 Feb 2022 11:37:02 UTC (17 KB)
[v3] Tue, 19 Mar 2024 11:17:40 UTC (18 KB)
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