Non-commutative deformations of tilting bundles and the derived McKay correspondence

TL;DR

This paper demonstrates that tilting bundles and the derived McKay correspondence can be extended to formal non-commutative deformations using Cech cohomology of non-commutative schemes.

Contribution

It introduces a method to extend tilting bundles and the derived McKay correspondence to non-commutative deformations via Cech cohomology.

Findings

Extension of tilting bundles to non-commutative deformations

Extension of derived McKay correspondence to non-commutative deformations

Use of Cech cohomology in non-commutative scheme context

Abstract

We prove that the tilting bundle and the derived McKay correspondence extends under formal non-commutative deformations by using Cech cohomology of non-commutative schemes.