Published on *Max Planck Institute for Mathematics* (http://www.mpim-bonn.mpg.de)

Posted in

- Talk [1]

Speaker:

Magali Rocher
Affiliation:

U de Bordeaux I / MPI
Date:

Wed, 10/02/2010 - 14:15 - 15:15 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 G be a p-subgroup of the k-automorphism group of C such that |G| > 2pg/(p-1). Then, C -->C/G is an étale cover of the affine line Spec k[X] totally ramified at infinity. To study such actions, we focus on the second ramification group G_2 of G at infinity, knowing that G_2 actually coincides with the derived group of G. We first display realizations of such actions with G_2 abelian of arbitrary large exponent . Our examples come from the construction of curves with many rational points using ray class field theory for global function fields. Then, considering additive polynomials of k[X], we obtain a structure theorem for the functions parametrizing the Artin-Schreier cover C --> C/G_2, in the case of a p-elementary abelian G_2. We finally emphasize the link between the curves obtained in this last case and supersingular curves (i.e. curves whose Jacobian is isogeneous to a product of supersingular elliptic curves).

**Links:**

[1] http://www.mpim-bonn.mpg.de/taxonomy/term/39

[2] http://www.mpim-bonn.mpg.de/node/3444

[3] http://www.mpim-bonn.mpg.de/node/246