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Liftings of Galois Covers of Smooth Curves

Published online by Cambridge University Press:  04 December 2007

BARRY GREEN  and
MICHEL MATIGNON
BARRY GREEN
Affiliation:
Department of Mathematics, University of Stellenbosch, Stellenbosch, 7602, South Africa; e-mail: bwg@land.sun.ac.za
MICHEL MATIGNON
Affiliation:
Mathématiques Pures de Bordeaux, E.R.S. 0127 C.N.R.S., Université de Bordeaux I, 351, cours de la Libération, 33405 – Talence, Cedex, France; e-mail: matignon@math.u-bordeaux.fr
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Abstract

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Let (C,G) be a smooth irreducible projective curve of genus g over an algebraically closed field k of chararacteristic p>0 and G be a finite group of automorphisms of C. It is well known that here, contrary to the characteristic 0 case, Hurwitz‘s bound |G|[les ] 84(g-1) doesn‘t hold in general; in such cases this gives an obstruction to obtaining a smooth galois lifting of (C,G) to characteristic 0. We shall give new obstructions of local nature to the lifting problem, even in the case where G is abelian. In the case where the inertia groups are p$^ae$-cyclic with a[les ] 2 and (e,p)=1, we shall prove that smooth galois liftings exist over W(k)[$^p^^2$√1].

Keywords

Sekiguchi–Suwa theoryorder p$^2$ automorphisms of p-adic discsrigid analytic geometry.
Type
Research Article
Information
Compositio Mathematica , Volume 113 , Issue 3 , September 1998 , pp. 237 - 272
Copyright
© 1998 Kluwer Academic Publishers