Thursday, October 19, 16:30, 8.122 (colloquium).
Frauke Bleher (University of Iowa)
Galois structure of the holomorphic
differential of curves.
This talk is about joint work with Ted Chinburg and Aristides Kontogeorgis on
module structure of the holomorphic differentials of the top curve of a finite
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
a Sylow p-subgroup of the Galois group is cyclic, the Galois module structure
holomorphic differentials can be effectively determined by ramification data
alone. I will
illustrate the results with an example involving a modular curve mod p.