title: Aspherical neighborhoods on arithmetic surfaces
creator: Hübner, Katharina
description: On arithmetic surfaces over local or global rings of integers this thesis examines whether a geometric point has a basis of étale neighborhoods which are aspherical with respect to a full class of finite groups c. In this thesis we will consider only classes of finite groups c such that the order of all groups in c is prime to the residue characteristics of the arithmetic surface in question. In the local case we construct a basis of aspherical neighborhoods for any geometric point of a normal (but not necessarily regular) arithmetic surface. In the global case the existence of such bases of neighborhoods is proven under additional regularity assumptions and a condition on the l-division points of the Jacobian of the generic fibre. Moreover, we assume in the global case case that c is the class of finite l-groups for a prime number l that is invertible on the arithmetic surface.
date: 2016-04-22
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/20585/1/diss.pdf
identifier: DOI:10.11588/heidok.00020585
identifier: urn:nbn:de:bsz:16-heidok-205854
identifier:   Hübner, Katharina  (2016) Aspherical neighborhoods on arithmetic surfaces.  [Dissertation]     
relation: https://archiv.ub.uni-heidelberg.de/volltextserver/20585/
rights: info:eu-repo/semantics/openAccess
rights: http://archiv.ub.uni-heidelberg.de/volltextserver/help/license_urhg.html
language: eng