The minimal model program for arithmetic surfaces enriched by a Brauer class
Algebraic Geometry
2021-08-09 v1 Rings and Algebras
Abstract
We examine the noncommutative minimal model program for orders on arithmetic surfaces, or equivalently, arithmetic surfaces enriched by a Brauer class . When has prime index , we show the classical theory extends with analogues of existence of terminal resolutions, Castelnuovo contraction and Zariski factorisation. We also classify -terminal surfaces and Castelnuovo contractions, and discover new unexpected behaviour.
Cite
@article{arxiv.2108.03105,
title = {The minimal model program for arithmetic surfaces enriched by a Brauer class},
author = {Daniel Chan and Colin Ingalls},
journal= {arXiv preprint arXiv:2108.03105},
year = {2021}
}