Large p-groups actions with |G| /g^2 > 4/ (p^2-1)^2.

Magali Rocher (1)

1 IMB - Institut de Mathématiques de Bordeaux

Let k be an algebraically closed field of characteristic p>0 and C a connected nonsingular projective curve over k with genus g>1. Let (C,G) be a "big action" , i.e. a pair (C,G) where G is a p-subgroup of the k-automorphism group of C such that |G|/g > 2p / p-1. We first study finiteness results on the values taken by the quotient |G|/g^2 when (C,G) runs over the big actions satisfying |G|/g^2 >M , for a given positive real M>0. Then, we exhibit a classification and a parametrization of such big actions when M=4/ (p^2-1)^2.

Domaines: Géométrie algébrique [math.AG]; Théorie des nombres [math.NT]

Magali Rocher. Large p-groups actions with |G| /g^2 > 4/ (p^2-1)^2.. 2008. ⟨hal-00274769⟩