2026-09-20T11:55:15Zhttps://dspace.mit.edu/server/oai/requestoai:dspace.mit.edu:1721.1/1178832026-06-16T18:14:24Zcom_1721.1_7582com_1721.1_7581col_1721.1_131022
Bjorn Poonen.
Bell, Renee Hyunjeong
Massachusetts Institute of Technology. Department of Mathematics.
Massachusetts Institute of Technology. Department of Mathematics
2018-09-17T15:48:27Z
2018-09-17T15:48:27Z
2018
2018
http://hdl.handle.net/1721.1/117883
1051190601
Thesis: Ph. D., Massachusetts Institute of Technology, Department of Mathematics, 2018.
Cataloged from PDF version of thesis.
Includes bibliographical references (page 41).
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.
by Renee Hyunjeong Bell.
Ph.D.
41 pages
eng
Massachusetts Institute of Technology
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.
http://dspace.mit.edu/handle/1721.1/7582
Mathematics.
Local-to-Global extensions for wildly ramified covers of curves
Thesis
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<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.</Abstract>
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