Galois-Module Theory for Wildly Ramified Covers of Curves over Finite Fields (with an Appendix by Bernhard Köck and Adriano Marmora)

  • Helena Fischbacher-Weitz

    Mathematical Sciences, University of Southampton, Southampton SO17 1BJ, United Kingdom
  • Bernhard Köck

    Mathematical Sciences, University of Southampton, Southampton SO17 1BJ, United Kingdom
  • Adriano Marmora

    Institut de Recherche Mathématique Avancée, Université de Strasbourg, 7 rue René Descartes, 67084 Strasbourg, France
Galois-Module Theory for Wildly Ramified Covers of Curves over Finite Fields (with an Appendix by Bernhard Köck and Adriano Marmora) cover
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Abstract

Given a Galois cover of curves over , we relate the -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 -adic valuations of epsilon constants.

Cite this article

Helena Fischbacher-Weitz, Bernhard Köck, Adriano Marmora, Galois-Module Theory for Wildly Ramified Covers of Curves over Finite Fields (with an Appendix by Bernhard Köck and Adriano Marmora). Doc. Math. 24 (2019), pp. 175–208

DOI 10.4171/DM/678