Noncommutative resolutions using syzygies

TL;DR

This paper introduces a general method for constructing new noncommutative resolutions from existing ones, utilizing syzygies, and demonstrates its application to modules over regular rings.

Contribution

It provides a novel construction technique for noncommutative resolutions using syzygies, expanding the toolkit for algebraic geometry and representation theory.

Findings

Any finite length module over a regular local or polynomial ring yields a noncommutative resolution via syzygies.

The construction generalizes existing methods for noncommutative resolutions.

Application to regular rings broadens the scope of noncommutative algebra techniques.

Abstract

Given a noether algebra with a noncommutative resolution, a general construction of new noncommutative resolutions is given. As an application, it is proved that any finite length module over a regular local or polynomial ring gives rise, via suitable syzygies, to a noncommutative resolution.