%0 Journal Article
%T The Explicit Construction of Orders on Surfaces
%A Hugo Bowne-Anderson
%J Mathematics
%D 2011
%I arXiv
%X We implement a noncommutative analogue of the well-known commutative cyclic covering trick and implement it to explicitly construct a vast collection of numerically Calabi-Yau orders, noncommutative analogues of surfaces of Kodaira dimension 0. We construct maximal orders, noncommutative analogues of normal schemes, on rational surfaces and ruled surfaces. We also use Ogg-Shafarevich theory to construct Azumaya algebras and, more generally, maximal orders on elliptically fibred surfaces.
%U http://arxiv.org/abs/1106.6279v1