Thursday, October 19, 16:30, 8.122 (colloquium).

Frauke Bleher (University of Iowa)
Galois structure of the holomorphic differential of curves.

Abstract:
This talk is about joint work with Ted Chinburg and Aristides Kontogeorgis on the Galois module structure of the holomorphic differentials of the top curve of a finite Galois cover of curves in positive characteristic p. The case in which p divides the order of the group is more subtle, since then not all representations are semi-simple. We show that when a Sylow p-subgroup of the Galois group is cyclic, the Galois module structure of the holomorphic differentials can be effectively determined by ramification data alone. I will illustrate the results with an example involving a modular curve mod p.