Conductors of wildly ramified covers, II
[Conducteurs des revêtements avec ramification sauvage, II]
Pries, Rachel J.1
1 Department of Mathematics, Columbia University, New York, NY 10027, USA
Comptes Rendus. Mathématique, Tome 335 (2002) no. 5, pp. 485-487.

Soit k un corps algébriquement clos de caractéristique p. Soit ϕ:Y→ℙ k 1 un revêtement fini galoisien, de groupe G, ramifié seulement au-dessus d'un point (avec ramification sauvage). On montre l'existence d'un revêtement de ce type avec tous conducteurs suffisamment grands quand les p-Sylow de G sont d'ordre p. La démonstration consiste à étudier la géométrie formelle.

Consider a wildly ramified G-Galois cover of curves ϕ:Y→ℙ k 1 branched at only one point over an algebraically closed field k of characteristic p. In this note, I prove using formal patching that all sufficiently large conductors occur for such covers φ when the Sylow p-subgroups of G have order p.

Reçu le :
Accepté le :
Publié le :
DOI : 10.1016/S1631-073X(02)02492-5
Pries, Rachel J. 1

1 Department of Mathematics, Columbia University, New York, NY 10027, USA 
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Pries, Rachel J. Conductors of wildly ramified covers, II. Comptes Rendus. Mathématique, Tome 335 (2002) no. 5, pp. 485-487. doi : 10.1016/S1631-073X(02)02492-5. http://archive.numdam.org/articles/10.1016/S1631-073X(02)02492-5/

[1] Fried, M.; Jarden, M. Field Arithmetic, Springer-Verlag, Berlin, 1986

[2] Harbater, D. Abhyankar's conjecture on Galois groups over curves, Invent. Math., Volume 117 (1994) no. 1, pp. 1-25

[3] Harbater, D.; Stevenson, K. Patching and thickening problems, J. Algebra, Volume 212 (1999) no. 1, pp. 272-304

[4] R. Pries, Conductors of wildly ramified covers, I, Preprint, 2001

[5] R. Pries, Conductors of wildly ramified covers, III, Preprint, 2001

[6] R. Pries, Families of wildly ramified covers of curves, Amer. J. Math., accepted

[7] Raynaud, M. Revêtements de la droite affine en caractéristique p>0 et conjecture d'Abhyankar, Invent. Math., Volume 116 (1994) no. 1–3, pp. 425-462

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