Local-to-Global extensions for wildly ramified covers of curves

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 fields comes from a global cover of Y in this way. Harbater proved that over a separably closed field, every Laurent series extension comes from a global cover for any base curve if G is a p-group, and he 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 extension property holds and for which it is unique up to isomorphism, but over a more general ground field.

Department dc:contributor.department

Massachusetts Institute of Technology. Department of Mathematics.

Grantor dc:publisher

Massachusetts Institute of Technology

Year dc:date.issued

2018

Author dc:creator

• Bell, Renee Hyunjeong

Advisor dc:contributor.advisor

• Bjorn Poonen.

• Mathematics.

Statement dc:rights

• MIT theses are protected by copyright. They may be viewed, downloaded, or printed from this source but further reproduction or distribution in any format is prohibited without written permission.

Licence dc:rights.uri

• http://dspace.mit.edu/handle/1721.1/7582

Language dc:language.iso

eng

Handle dc:identifier.uri

http://hdl.handle.net/1721.1/117883

OAI identifier oai:identifier

oai:dspace.mit.edu:1721.1/117883