{"id":{"repo_id":"heid-diss","oai_identifier":"oai:archiv.ub.uni-heidelberg.de:7179"},"canonical_url":"https://search.dev.ndltd.org/etd/heid-diss/oai:archiv.ub.uni-heidelberg.de:7179","repository":{"repo_id":"heid-diss","name":"Universität Heidelberg","base_url":"http://archiv.ub.uni-heidelberg.de/volltextserver/cgi/oai2"},"display":{"title":"Iterative Connections and Abhyankar's Conjecture","abstract":"This thesis contains two major parts. In the first part, I introduce a new theory of modules with iterative connection. This theory unifies the theory of modules with connection in characteristic zero as given by N. Katz and the theory of iterative differential modules in positive characteristic as given by B. H. Matzat und M. van der Put. The second part of this work is about the differential Abhyankar conjecture for iterative Picard-Vessiot extensions (IPV-extensions). This conjecture is concerned with the problem which linear algebraic groups occur as iterative differential Galois groups of IPV-extensions with restricted singular locus. In this thesis, I prove the differential Abhyankar conjecture for connected groups and give necessary and sufficient conditions for connected groups for being realisable with given singular points.","abstract_html":"This thesis contains two major parts. In the first part, I introduce a new theory of modules with iterative connection. This theory unifies the theory of modules with connection in characteristic zero as given by N. Katz and the theory of iterative differential modules in positive characteristic as given by B. H. Matzat und M. van der Put. The second part of this work is about the differential Abhyankar conjecture for iterative Picard-Vessiot extensions (IPV-extensions). This conjecture is concerned with the problem which linear algebraic groups occur as iterative differential Galois groups of IPV-extensions with restricted singular locus. In this thesis, I prove the differential Abhyankar conjecture for connected groups and give necessary and sufficient conditions for connected groups for being realisable with given singular points.","abstract_has_math":false,"creators":["Röscheisen, Andreas"],"institution":"Universität Heidelberg","degree_name":null,"degree_level":"thesis.doctoral","degree_discipline":null,"degree_department":null,"school":null,"contributors":["Matzat, B. Heinrich"],"advisors":[],"committee_chairs":[],"committee_members":[],"year":2007,"date_issued":"2007-01-30","date_published":"2007-01-30","updated_at":"2026-07-24T02:30:41Z","subjects":[],"languages":[],"rights":[],"rights_urls":[],"identifier_entries":[]},"links":{"outbound_url":"http://www.ub.uni-heidelberg.de/archiv/7179","outbound_label":"Repository record","outbound_source":"source_url"},"metadata_groups":[{"id":"people","label":"People","entries":[{"key":"dc:contributor","label":"Contributor","values":["Matzat, B. Heinrich"]},{"key":"dc:creator","label":"Author","values":["Röscheisen, Andreas"]}]},{"id":"academic_context","label":"Academic Context","entries":[{"key":"dc:publisher","label":"Institution","values":["Universitätsbibliothek Heidelberg"]},{"key":"dc:type","label":"Dc Type","values":["doctoralThesis"]},{"key":"thesis:degree_level","label":"Degree Level","values":["thesis.doctoral"]},{"key":"thesis:institution_name","label":"Thesis Institution Name","values":["Universität Heidelberg"]}]},{"id":"additional","label":"Additional Metadata","entries":[{"key":"dc:description.abstract","label":"Abstract","values":["This thesis contains two major parts. In the first part, I introduce a new theory of modules with iterative connection. This theory unifies the theory of modules with connection in characteristic zero as given by N. Katz and the theory of iterative differential modules in positive characteristic as given by B. H. Matzat und M. van der Put. The second part of this work is about the differential Abhyankar conjecture for iterative Picard-Vessiot extensions (IPV-extensions). This conjecture is concerned with the problem which linear algebraic groups occur as iterative differential Galois groups of IPV-extensions with restricted singular locus. In this thesis, I prove the differential Abhyankar conjecture for connected groups and give necessary and sufficient conditions for connected groups for being realisable with given singular points.","Diese Doktorarbeit besteht im Großen aus zwei Teilen. Im ersten Teil entwickle ich eine neue Theorie von Moduln mit iterativem Zusammenhang. Diese Theorie vereinheitlicht die Theorie der Moduln mit Zusammenhang in Charakteristik Null, wie N. Katz sie vorstellt, und die Theorie der iterativen Differential-Moduln von B. H. Matzat und M. van der Put. Im zweiten Teil der Arbeit geht es um die Differential-Abhyankar-Vermutung für iterative Picard-Vessiot-Erweiterungen (IPV-Erweiterungen). Diese Vermutung macht darüber Aussagen, welche lineare algebraische Gruppe als iterative Differential-Galoisgruppe von IPV-Erweiterungen mit eingeschränktem singulären Ort vorkommen. In dieser Arbeit beweise ich die Differential-Abhyankar-Vermutung für zusammenhängende Gruppen und gebe notwendige und hinreichende Kriterien für die Realisierbarkeit zusammenhängender Gruppen mit vorgegebenen Singularitäten an."]},{"key":"dc:format.medium","label":"Dc Format Medium","values":["application/pdf"]},{"key":"dc:title","label":"Title","values":["Iterative Connections and Abhyankar's Conjecture","Iterative Zusammenhänge und Abhyankars Vermutung"]}]}],"canonical_facts":{"dc:contributor":["Matzat, B. Heinrich"],"dc:creator":["Röscheisen, Andreas"],"dc:description.abstract":["This thesis contains two major parts. In the first part, I introduce a new theory of modules with iterative connection. This theory unifies the theory of modules with connection in characteristic zero as given by N. Katz and the theory of iterative differential modules in positive characteristic as given by B. H. Matzat und M. van der Put. The second part of this work is about the differential Abhyankar conjecture for iterative Picard-Vessiot extensions (IPV-extensions). This conjecture is concerned with the problem which linear algebraic groups occur as iterative differential Galois groups of IPV-extensions with restricted singular locus. In this thesis, I prove the differential Abhyankar conjecture for connected groups and give necessary and sufficient conditions for connected groups for being realisable with given singular points.","Diese Doktorarbeit besteht im Großen aus zwei Teilen. Im ersten Teil entwickle ich eine neue Theorie von Moduln mit iterativem Zusammenhang. Diese Theorie vereinheitlicht die Theorie der Moduln mit Zusammenhang in Charakteristik Null, wie N. Katz sie vorstellt, und die Theorie der iterativen Differential-Moduln von B. H. Matzat und M. van der Put. Im zweiten Teil der Arbeit geht es um die Differential-Abhyankar-Vermutung für iterative Picard-Vessiot-Erweiterungen (IPV-Erweiterungen). Diese Vermutung macht darüber Aussagen, welche lineare algebraische Gruppe als iterative Differential-Galoisgruppe von IPV-Erweiterungen mit eingeschränktem singulären Ort vorkommen. In dieser Arbeit beweise ich die Differential-Abhyankar-Vermutung für zusammenhängende Gruppen und gebe notwendige und hinreichende Kriterien für die Realisierbarkeit zusammenhängender Gruppen mit vorgegebenen Singularitäten an."],"dc:format.medium":["application/pdf"],"dc:publisher":["Universitätsbibliothek Heidelberg"],"dc:title":["Iterative Connections and Abhyankar's Conjecture","Iterative Zusammenhänge und Abhyankars Vermutung"],"dc:type":["doctoralThesis"],"thesis:degree_level":["thesis.doctoral"],"thesis:institution_name":["Universität Heidelberg"]},"updated_at":"2026-07-24T02:30:41Z"}