### Local-to-Global lifting to curves in characterstic p

- Series
- Algebra Seminar
- Time
- Monday, November 13, 2017 - 15:00 for 1 hour (actually 50 minutes)
- Location
- Skiles 006
- Speaker
- Renee Bell – Massachusetts Institute of Technology – rhbell@math.mit.edu

Given a Galois cover of curves X to 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 this lifting property holds and when it is unique, but over
a more general ground field.