Non-commutative crepant resolutions
Michel Van den Bergh
TL;DR
This paper introduces non-commutative crepant resolutions for singularities, demonstrating their existence in specific cases and providing evidence supporting a conjecture that different crepant resolutions share the same derived category.
Contribution
It defines non-commutative crepant resolutions and shows their existence, extending the understanding of derived categories in singularity resolutions.
Findings
Existence of non-commutative crepant resolutions in certain cases
Support for the conjecture that different crepant resolutions have equivalent derived categories
Extension of Bondal and Orlov's conjecture to non-commutative settings
Abstract
We introduce the notion of a ``non-commutative crepant'' resolution of a singularity and show that it exists in certain cases. We also give some evidence for an extension of a conjecture by Bondal and Orlov, stating that different crepant resolutions of a Gorenstein singularity have the same derived category.
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Taxonomy
TopicsAlgebraic structures and combinatorial models · Homotopy and Cohomology in Algebraic Topology · Algebraic Geometry and Number Theory