title: Iterative Connections and Abhyankar's Conjecture
creator: Röscheisen, Andreas
subject: ddc-510
subject: 510 Mathematics
description: 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.
date: 2006
type: Dissertation
type: info:eu-repo/semantics/doctoralThesis
type: NonPeerReviewed
format: application/pdf
identifier: https://archiv.ub.uni-heidelberg.de/volltextserverhttps://archiv.ub.uni-heidelberg.de/volltextserver/7179/1/diss.pdf
identifier: DOI:10.11588/heidok.00007179
identifier: urn:nbn:de:bsz:16-opus-71796
identifier:   Röscheisen, Andreas  (2006) Iterative Connections and Abhyankar's Conjecture.  [Dissertation]     
relation: https://archiv.ub.uni-heidelberg.de/volltextserver/7179/
rights: info:eu-repo/semantics/openAccess
rights: http://archiv.ub.uni-heidelberg.de/volltextserver/help/license_urhg.html
language: eng