  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.

Algebraic Geometry;Number Theory