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Galois-module theory for wildly ramified covers of curves over finite fields: [With an appendix by Bernhard Koeck and Adriano Marmora: Integrality of epsilon representations of wildly ramified Galois covers]

Galois-module theory for wildly ramified covers of curves over finite fields: [With an appendix by Bernhard Koeck and Adriano Marmora: Integrality of epsilon representations of wildly ramified Galois covers]
Galois-module theory for wildly ramified covers of curves over finite fields: [With an appendix by Bernhard Koeck and Adriano Marmora: Integrality of epsilon representations of wildly ramified Galois covers]
Given a Galois cover of curves over F_p , we relate the p-adic valuation of epsilon constants appearing in functional equations of Artin
L-functions to an equivariant Euler characteristic. Our main theorem generalises a result of Chinburg from the tamely to the weakly ramified case. We furthermore apply Chinburg’s result to obtain a ‘weak’ relation in the general case. In the Appendix, we study, in this arbitrarily wildly ramified case, the integrality of p-adic valuations of epsilon constants.
Galois cover of curves, weakly ramified, epsilon constant, equivariant Euler characteristic
1431-0635
175-208
Fischbacher-Weitz, Helena B.
8cf9dd19-8bad-4d46-8fd1-d7be8ac7026f
Koeck, Bernhard
84d11519-7828-43a6-852b-0c1b80edeef9
Marmora, Adriano
6f1cf393-8f51-41bb-b553-9787c2706adb
Fischbacher-Weitz, Helena B.
8cf9dd19-8bad-4d46-8fd1-d7be8ac7026f
Koeck, Bernhard
84d11519-7828-43a6-852b-0c1b80edeef9
Marmora, Adriano
6f1cf393-8f51-41bb-b553-9787c2706adb

Fischbacher-Weitz, Helena B., Koeck, Bernhard and Marmora, Adriano (2019) Galois-module theory for wildly ramified covers of curves over finite fields: [With an appendix by Bernhard Koeck and Adriano Marmora: Integrality of epsilon representations of wildly ramified Galois covers]. Documenta Mathematica, 24, 175-208.

Record type: Article

Abstract

Given a Galois cover of curves over F_p , we relate the p-adic valuation of epsilon constants appearing in functional equations of Artin
L-functions to an equivariant Euler characteristic. Our main theorem generalises a result of Chinburg from the tamely to the weakly ramified case. We furthermore apply Chinburg’s result to obtain a ‘weak’ relation in the general case. In the Appendix, we study, in this arbitrarily wildly ramified case, the integrality of p-adic valuations of epsilon constants.

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More information

In preparation date: 12 December 2014
Accepted/In Press date: 19 January 2019
Published date: 15 April 2019
Keywords: Galois cover of curves, weakly ramified, epsilon constant, equivariant Euler characteristic
Organisations: Pure Mathematics

Identifiers

Local EPrints ID: 372706
URI: https://eprints.soton.ac.uk/id/eprint/372706
ISSN: 1431-0635
PURE UUID: 182884ca-03d3-4495-8809-51d7a18e1b95

Catalogue record

Date deposited: 18 Dec 2014 11:23
Last modified: 16 May 2019 16:31

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