Comptes Rendus
Conductors of wildly ramified covers, I
Comptes Rendus. Mathématique, Volume 335 (2002) no. 5, pp. 481-484.

Consider a wildly ramified G-Galois cover of curves ϕ:Y k 1 branched at only one point over an algebraically closed field k of characteristic p. For any p-pure group G whose Sylow p-subgroups have order p, I show the existence of such a cover with small conductor. The proof uses an analysis of the semi-stable reduction of families of covers.

Soit k un corps algébriquement clos de caractéristique p. Soit ϕ:Y k 1 un revêtement fini galoisien, de groupe G, ramifié seulement au-dessus d'un point (avec ramification sauvage). Quand G est p-pur et les p-Sylow de G sont d'ordre p, on montre qu'il existe un revêtement de ce type avec un conducteur petit. La démonstration consiste à étudier la réduction semi-stable des familles des revêtements.

Received:
Accepted:
Published online:
DOI: 10.1016/S1631-073X(02)02491-3

Rachel J. Pries 1

1 Department of Mathematics, Columbia University, New York, NY 10027, USA
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Rachel J. Pries. Conductors of wildly ramified covers, I. Comptes Rendus. Mathématique, Volume 335 (2002) no. 5, pp. 481-484. doi : 10.1016/S1631-073X(02)02491-3. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.1016/S1631-073X(02)02491-3/

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