Maximal orders in unramified central simple algebras

TL;DR

This paper constructs non-Azumaya maximal orders in unramified central simple algebras over schemes of dimension three or higher using depth of coherent sheaves on algebraic stacks.

Contribution

It introduces a novel method leveraging algebraic stacks and sheaf depth to produce examples of maximal orders that are not Azumaya.

Findings

Existence of non-Azumaya maximal orders in specified algebras.

Application of algebraic stack techniques to order construction.

Extension of known results to higher-dimensional schemes.

Abstract

Using depth of coherent sheaves on noetherian algebraic stacks, we construct non-Azumaya maximal orders in unramified central simple algebras over schemes of dimension at least $3$.