{"id":{"repo_id":"uiuc","oai_identifier":"oai:www.ideals.illinois.edu:2142/23755"},"canonical_url":"https://search.dev.ndltd.org/etd/uiuc/oai:www.ideals.illinois.edu:2142/23755","repository":{"repo_id":"uiuc","name":"University of Illinois - Urbana-Champaign","base_url":"https://www.ideals.illinois.edu/oai-pmh"},"display":{"title":"Toward a deformation theory for Galois representations of function fields","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.","abstract_html":"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.","abstract_has_math":false,"creators":["Ose, David Thomas"],"institution":"University of Illinois at Urbana-Champaign","degree_name":"Ph.D.","degree_level":"Dissertation","degree_discipline":"Mathematics","degree_department":null,"school":null,"contributors":["Boston, Nigel"],"advisors":[],"committee_chairs":[],"committee_members":[],"year":2011,"date_issued":"2011-05-07T14:25:53Z","date_published":"2011-05-07T14:25:53Z","updated_at":"2026-07-22T22:25:22Z","subjects":["Mathematics"],"languages":["eng"],"rights":["Copyright 1995 Ose, David Thomas"],"rights_urls":[],"identifier_entries":[{"key":"dc:identifier","label":"Identifier","values":["AAI9624453","(UMI)AAI9624453"],"render_values":[{"text":"AAI9624453","href":null,"code":true},{"text":"(UMI)AAI9624453","href":null,"code":true}]}]},"links":{"outbound_url":"http://hdl.handle.net/2142/23755","outbound_label":"Handle","outbound_source":"dc:identifier"},"metadata_groups":[{"id":"people","label":"People","entries":[{"key":"dc:contributor","label":"Contributor","values":["Boston, Nigel"]},{"key":"dc:creator","label":"Author","values":["Ose, David Thomas"]}]},{"id":"academic_context","label":"Academic Context","entries":[{"key":"dc:date","label":"Dc Date","values":["2011-05-07T14:25:53Z","10000-01-01","1995"]},{"key":"dc:type","label":"Dc Type","values":["text"]},{"key":"thesis:degree_discipline","label":"Discipline","values":["Mathematics"]},{"key":"thesis:degree_level","label":"Degree Level","values":["Dissertation"]},{"key":"thesis:degree_name","label":"Degree Name","values":["Ph.D."]},{"key":"thesis:institution_name","label":"Thesis Institution Name","values":["University of Illinois at Urbana-Champaign"]}]},{"id":"subjects_keywords","label":"Subjects and Keywords","entries":[{"key":"dc:subject","label":"Dc Subject","values":["Mathematics"]}]},{"id":"language_rights","label":"Language and Rights","entries":[{"key":"dc:language","label":"Dc Language","values":["eng"]},{"key":"dc:rights","label":"Dc Rights","values":["Copyright 1995 Ose, David Thomas"]}]},{"id":"identifiers","label":"Identifiers","entries":[{"key":"dc:identifier","label":"Identifier","values":["AAI9624453","(UMI)AAI9624453","http://hdl.handle.net/2142/23755"]}]},{"id":"additional","label":"Additional Metadata","entries":[{"key":"dc:description","label":"Description","values":["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. 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