Galois-module theory for wildly ramified covers of curves over finite fields

Abstract

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.

v2: Appendix by Bernhard Köck and Adriano Marmmora added, mistake in earlier generalised version of Lemma 2.6 removed, further mainly editorial changes; v3: this final, somewhat shortened version is to appear in Documenta Mathematica, 33p