The Explicit Construction of Orders on Surfaces
Algebraic Geometry
2011-07-01 v1 Rings and Algebras
Abstract
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.
Cite
@article{arxiv.1106.6279,
title = {The Explicit Construction of Orders on Surfaces},
author = {Hugo Bowne-Anderson},
journal= {arXiv preprint arXiv:1106.6279},
year = {2011}
}
Comments
94 pages, 8 figures, Ph.D. thesis, University of New South Wales (supervisor: Dr Daniel Chan)