Non-commutative crepant resolutions, an overview

2022/07/20 by Michel Van den Bergh, Bergh, Michel Van den · 4 citations
Mathematics · #Rings, Modules, and Algebras #Homotopy and Cohomology in Algebraic Topology #Geometric and Algebraic Topology

paper · pdf · doi:10.48550/arxiv.2207.09703

Abstract

Non-commutative crepant resolutions (NCCRs) are non-commutative analogues of the usual crepant resolutions that appear in algebraic geometry. In this paper we survey some results around NCCRs.

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• Non-commutative crepant resolutions of toric singularities with divisor class group of rank one
• Towards non-commutative crepant resolutions of affine toric Gorenstein varieties
• Silting correspondences and Calabi-Yau dg algebras
• Derived equivalence for the simple flop of type D₄ via tilting bundles

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