# Algebraic Geometry Seminar

#### Local-To-Global Principles for Galois Covers of Curves in Characteristic P

Speaker: Renee Bell, MIT

Location: Warren Weaver Hall 201

Date: Tuesday, April 25, 2017, 3:30 p.m.

Synopsis:

Given a Galois cover of curves X->Y with Galois group G which is totally ramified at a point x and unramified elsewhere, restriction to the punctured formal neighborhood of x induces a Galois extension of Laurent series rings k((u))/k((t)). If we fix a base curve Y, we can ask when a Galois extension of Laurent series rings comes from a global cover of Y in this way. Harbater proved that over a separably closed field, this local-to-global principle holds for any base curve if G is a p-group, and gave a condition for the uniqueness of such an extension. Using a generalization of Artin-Schreier theory to non-abelian p-groups, we characterize the curves Y for which an extension to a global cover of curves is unique over a more general ground field.