%0 Generic
%A Hübner, Katharina
%D 2016
%F heidok:20585
%R 10.11588/heidok.00020585
%T Aspherical neighborhoods on arithmetic surfaces
%U https://archiv.ub.uni-heidelberg.de/volltextserver/20585/
%X 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.