Conductors of wildly ramified covers, II

Rachel J. Pries

doi:10.1016/S1631-073X(02)02492-5

Conductors of wildly ramified covers, II
[Conducteurs des revêtements avec ramification sauvage, II]

Rachel J. Pries ¹

¹ Department of Mathematics, Columbia University, New York, NY 10027, USA

Comptes Rendus. Mathématique, Volume 335 (2002) no. 5, pp. 485-487.

Résumé
Abstract

Soit k un corps algébriquement clos de caractéristique p. Soit $ϕ : Y \to ℙ_{k}^{1}$ 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 $ϕ : Y \to ℙ_{k}^{1}$ 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 : 2002-06-10
Accepté le : 2002-06-20
Publié le : 2002-01-01

DOI : 10.1016/S1631-073X(02)02492-5

Affiliations des auteurs :

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, II. Comptes Rendus. Mathématique, Volume 335 (2002) no. 5, pp. 485-487. doi : 10.1016/S1631-073X(02)02492-5. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.1016/S1631-073X(02)02492-5/

Bibliographie
Cité par

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

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

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

Jeremy Muskat; Rachel Pries Alternating group covers of the affine line, Israel Journal of Mathematics, Volume 187 (2012) no. 1, p. 117 | DOI:10.1007/s11856-011-0165-7
Rachel J. Pries Wildly ramified covers with large genus, Journal of Number Theory, Volume 119 (2006) no. 2, p. 194 | DOI:10.1016/j.jnt.2005.10.013
Rachel J. Pries Conductors of wildly ramified covers, II, Comptes Rendus. Mathématique, Volume 335 (2002) no. 5, p. 485 | DOI:10.1016/s1631-073x(02)02492-5

Cité par 3 documents. Sources : Crossref

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