Geodesic
Galois-Module Theory for Wildly Ramified Covers of Curves over Finite Fields (with an Appendix by Bernhard Köck and Adriano Marmora)
Documenta mathematica, Tome 24 (2019), pp. 175-208.

Voir la notice de l'article provenant de la source Electronic Library of Mathematics

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.
Classification : 11R58, 14G10, 14G15, 11R33, 14H30
Keywords: Galois cover of curves, weakly ramified, epsilon constant, equivariant Euler characteristic 
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     author = {Fischbacher-Weitz, Helena and K\"ock, Bernhard and Marmora, Adriano},
     title = {Galois-Module {Theory} for {Wildly} {Ramified} {Covers} of {Curves} over {Finite} {Fields} (with an {Appendix} by {Bernhard} {K\"ock} and {Adriano} {Marmora)}},
     journal = {Documenta mathematica},
     pages = {175--208},
     publisher = {mathdoc},
     volume = {24},
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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). Documenta mathematica, Tome 24 (2019), pp. 175-208. http://geodesic.mathdoc.fr/item/DOCMA_2019__24__a57/