Fischbacher-Weitz, Helena; Köck, Bernhard; Marmora, Adriano

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

Doc. Math. 24, 175-208 (2019)
DOI: 10.25537/dm.2019v24.175-208
Communicated by Takeshi Saito


Given a Galois cover of curves over \(\mathbb{F}_p\), 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.

Mathematics Subject Classification

11R58, 14G10, 14G15, 11R33, 14H30


Galois cover of curves, weakly ramified, epsilon constant, equivariant Euler characteristic


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Fischbacher-Weitz, Helena
Mathematical Sciences, University of Southampton, Southampton SO17 1BJ, United Kingdom
Köck, Bernhard
Mathematical Sciences, University of Southampton, Southampton SO17 1BJ, United Kingdom
Marmora, Adriano
Institut de Recherche Mathématique Avancée, Université de Strasbourg, 7 rue René Descartes, 67084 Strasbourg, France