English

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 β\beta. When β\beta has prime index p>5p>5, we show the classical theory extends with analogues of existence of terminal resolutions, Castelnuovo contraction and Zariski factorisation. We also classify β\beta-terminal surfaces and Castelnuovo contractions, and discover new unexpected behaviour.

Keywords

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}
}
R2 v1 2026-06-24T04:53:30.218Z