Galois-module theory for wildly ramified covers of curves over finite fields: (with an Appendix by Bernhard Köck and Adriano Marmora)
Galois-module theory for wildly ramified covers of curves over finite fields: (with an Appendix by Bernhard Köck and Adriano Marmora)
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
175-208
Fischbacher-Weitz, Helena B.
8cf9dd19-8bad-4d46-8fd1-d7be8ac7026f
Köck, Bernhard
84d11519-7828-43a6-852b-0c1b80edeef9
Marmora, Adriano
6f1cf393-8f51-41bb-b553-9787c2706adb
15 April 2019
Fischbacher-Weitz, Helena B.
8cf9dd19-8bad-4d46-8fd1-d7be8ac7026f
Köck, Bernhard
84d11519-7828-43a6-852b-0c1b80edeef9
Marmora, Adriano
6f1cf393-8f51-41bb-b553-9787c2706adb
Fischbacher-Weitz, Helena B., Köck, Bernhard and Marmora, Adriano
(2019)
Galois-module theory for wildly ramified covers of curves over finite fields: (with an Appendix by Bernhard Köck and Adriano Marmora).
Documenta Mathematica, 24, .
(doi:10.25537/dm.2019v24.175-208).
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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EpsilonConstant4
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EpsilonConstant7
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10011950000
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EpsilonConstantv1.pdf
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In preparation date: 12 December 2014
Accepted/In Press date: 19 January 2019
e-pub ahead of print date: 15 April 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: http://eprints.soton.ac.uk/id/eprint/372706
ISSN: 1431-0635
PURE UUID: 182884ca-03d3-4495-8809-51d7a18e1b95
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Date deposited: 18 Dec 2014 11:23
Last modified: 15 Mar 2024 03:10
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Author:
Helena B. Fischbacher-Weitz
Author:
Adriano Marmora
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