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arXiv · 1412.3406

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

Helena Fischbacher-Weitz·Bernhard Köck·Adriano Marmora
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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.

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Helena Fischbacher-Weitz, Bernhard Köck, Adriano Marmora. 2014-12-10. Galois-module theory for wildly ramified covers of curves over finite fields. https://arxiv.org/abs/1412.3406

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