Toward a deformation theory for Galois representations of function fields

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.

Name thesis:degree_name

Ph.D.

Level thesis:degree_level

Dissertation

Discipline thesis:degree_discipline

Mathematics

Grantor

University of Illinois at Urbana-Champaign

Year dc:date

2011

Author dc:creator

• Ose, David Thomas

Contributors dc:contributor

• Boston, Nigel

• Mathematics

Statement dc:rights

• Copyright 1995 Ose, David Thomas

Language dc:language

eng

Identifier

AAI9624453
(UMI)AAI9624453

OAI identifier oai:identifier

oai:www.ideals.illinois.edu:2142/23755