Local-to-Global extensions for wildly ramified covers of curves
Name
1051190601-MIT.pdf
Description
Full printable version
Size
1.87 MB
Format
Adobe PDF
Checksum (MD5)
60d6522c3c409d85212b05ad35e46eb1
Author(s)
Bell, Renee Hyunjeong
Advisor(s)
Bjorn Poonen.
Date Issued
2018
Publisher
Massachusetts Institute of Technology
Abstract
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.
Description
Thesis: Ph. D., Massachusetts Institute of Technology, Department of Mathematics, 2018.
Cataloged from PDF version of thesis.
Includes bibliographical references (page 41).
Subjects
Mathematics.
MIT Department
Massachusetts Institute of Technology. Department of Mathematics
Terms of Use
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