Local-to-Global extensions for wildly ramified covers of curves
Author(s)Bell, Renee Hyunjeong
Massachusetts Institute of Technology. Department of Mathematics.
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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.
Thesis: Ph. D., Massachusetts Institute of Technology, Department of Mathematics, 2018.Cataloged from PDF version of thesis.Includes bibliographical references (page 41).
DepartmentMassachusetts Institute of Technology. Department of Mathematics.
Massachusetts Institute of Technology