Toward a deformation theory for Galois representations of function fields
Ose, David Thomas
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https://hdl.handle.net/2142/23755
Description
Title
Toward a deformation theory for Galois representations of function fields
Author(s)
Ose, David Thomas
Issue Date
1995
Doctoral Committee Chair(s)
Boston, Nigel
Department of Study
Mathematics
Discipline
Mathematics
Degree Granting Institution
University of Illinois at Urbana-Champaign
Degree Name
Ph.D.
Degree Level
Dissertation
Keyword(s)
Mathematics
Language
eng
Abstract
We consider a question of describing the one-dimensional P-adic representations that lift a given representation over a finite field of the absolute Galois group of a function field K. In this case, the characterization of abelian p-power extensions of fields of characteristic p can be extended and refined to allow only restricted ramification at the places of K, and can be a tool for analyzing one-dimensional P-adic representations. We then turn to the problem of classifying those representations which can be realized as the action of the Galois group on the division points of a rank one Drinfeld module, discussing both results and a conjecture about form of the representations that arise in this manner.
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