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2008 Smooth curves having a large automorphism $p$-group in characteristic $p\gt 0$
Michel Matignon, Magali Rocher
Algebra Number Theory 2(8): 887-926 (2008). DOI: 10.2140/ant.2008.2.887


Let k be an algebraically closed field of characteristic p>0 and C a connected nonsingular projective curve over k with genus g2. This paper continues our study of big actions, that is, pairs (C,G) where G is a p-subgroup of the k-automorphism group of C such that |G|g>2p(p1). If G2 denotes the second ramification group of G at the unique ramification point of the cover CCG, we display necessary conditions on G2 for (C,G) to be a big action, which allows us to pursue the classification of big actions.

Our main source of examples comes from the construction of curves with many rational points using ray class field theory for global function fields, as initiated by J.-P. Serre and continued by Lauter and by Auer. In particular, we obtain explicit examples of big actions with G2 abelian of large exponent.


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Michel Matignon. Magali Rocher. "Smooth curves having a large automorphism $p$-group in characteristic $p\gt 0$." Algebra Number Theory 2 (8) 887 - 926, 2008.


Received: 1 February 2008; Revised: 14 August 2008; Accepted: 17 September 2008; Published: 2008
First available in Project Euclid: 20 December 2017

zbMATH: 1168.14023
MathSciNet: MR2457356
Digital Object Identifier: 10.2140/ant.2008.2.887

Primary: 14H37
Secondary: 11G20, 11R37, 14H10

Rights: Copyright © 2008 Mathematical Sciences Publishers


Vol.2 • No. 8 • 2008
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