Character formula for Weil representations in terms of Frobenius traces

Tim Dokchitser; Vladimir Dokchitser

doi:10.48550/arXiv.2201.04094

Character formula for Weil representations in terms of Frobenius traces

Tim Dokchitser^*, Vladimir Dokchitser

^*Corresponding author for this work

Research output: Chapter in Book/Report/Conference proceeding › Conference Contribution (Conference Proceeding)

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.

Original language	English
Title of host publication	Arithmetic of L-Functions
Subtitle of host publication	Proceedings of an International Conference held at ICMAT, Madrid, May 2023
Publisher	American Mathematical Society
Pages	101-111
Number of pages	11
ISBN (Electronic)	9783985475841
ISBN (Print)	9783985470846
DOIs	https://doi.org/10.48550/arXiv.2201.04094 https://doi.org/10.4171/ECR/20/4
Publication status	Published - 3 Mar 2025
Event	International conference on the Arithmetic of L‐functions - Instituto de Ciencias Matemáticas, Madrid, Spain Duration: 22 May 2023 → 26 May 2023 https://www.icmat.es/congresos/2023/AOLF/index.php

Publication series

Name	EMS Series of Congress Reports
Publisher	American Mathematical Society
ISSN (Print)	2523-515X
ISSN (Electronic)	2523-5168

Conference

Conference	International conference on the Arithmetic of L‐functions
Country/Territory	Spain
City	Madrid
Period	22/05/23 → 26/05/23
Internet address	https://www.icmat.es/congresos/2023/AOLF/index.php

Bibliographical note

7 pages

Keywords

math.NT
math.AG
11F80, 11G10, 11G20, 11G25, 14F20

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10.48550/arXiv.2201.04094Licence: CC BY
10.4171/ECR/20/4

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Accepted author manuscript, 350 KBLicence: CC BY

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Dokchitser, T., & Dokchitser, V. (2025). Character formula for Weil representations in terms of Frobenius traces. In Arithmetic of L-Functions: Proceedings of an International Conference held at ICMAT, Madrid, May 2023 (pp. 101-111). (EMS Series of Congress Reports). American Mathematical Society. https://doi.org/10.48550/arXiv.2201.04094, https://doi.org/10.4171/ECR/20/4

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title = "Character formula for Weil representations in terms of Frobenius traces",

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.",

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author = "Tim Dokchitser and Vladimir Dokchitser",

note = "7 pages; International conference on the Arithmetic of L‐functions ; Conference date: 22-05-2023 Through 26-05-2023",

year = "2025",

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doi = "10.48550/arXiv.2201.04094",

language = "English",

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series = "EMS Series of Congress Reports",

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Dokchitser, T & Dokchitser, V 2025, Character formula for Weil representations in terms of Frobenius traces. in Arithmetic of L-Functions: Proceedings of an International Conference held at ICMAT, Madrid, May 2023. EMS Series of Congress Reports, American Mathematical Society, pp. 101-111, International conference on the Arithmetic of L‐functions, Madrid, Spain, 22/05/23. https://doi.org/10.48550/arXiv.2201.04094, https://doi.org/10.4171/ECR/20/4

Character formula for Weil representations in terms of Frobenius traces. / Dokchitser, Tim; Dokchitser, Vladimir.
Arithmetic of L-Functions: Proceedings of an International Conference held at ICMAT, Madrid, May 2023. American Mathematical Society, 2025. p. 101-111 (EMS Series of Congress Reports).

Research output: Chapter in Book/Report/Conference proceeding › Conference Contribution (Conference Proceeding)

TY - GEN

T1 - Character formula for Weil representations in terms of Frobenius traces

AU - Dokchitser, Tim

AU - Dokchitser, Vladimir

N1 - 7 pages

PY - 2025/3/3

Y1 - 2025/3/3

N2 - 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.

AB - 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.

KW - math.NT

KW - math.AG

KW - 11F80, 11G10, 11G20, 11G25, 14F20

UR - https://www.icmat.es/congresos/2023/AOLF/index.php

U2 - 10.48550/arXiv.2201.04094

DO - 10.48550/arXiv.2201.04094

M3 - Conference Contribution (Conference Proceeding)

SN - 9783985470846

T3 - EMS Series of Congress Reports

SP - 101

EP - 111

BT - Arithmetic of L-Functions

PB - American Mathematical Society

T2 - International conference on the Arithmetic of L‐functions

Y2 - 22 May 2023 through 26 May 2023

ER -

Character formula for Weil representations in terms of Frobenius traces

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Bibliographical note

Keywords

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