Non-Commutative Crepant Resolutions: Scenes from Categorical Geometry
By Graham J. Leuschke. 2011
50 citations recorded by the source corpus.
Non-commutative crepant resolutions are algebraic objects defined by Van den Bergh to realize an equivalence of derived categories in birational geometry. They are motivated by tilting theory, the McKay correspondence, and the minimal model program, and have applications to string theory and representation theory. In this expository article I situate Van den Bergh's definition within these contexts and describe some of the current research in the area.
Subfields: Geometry and Topology, Mathematical Physics
View Paper: https://www.semanticscholar.org/paper/a1d851c36b32ca1fdd2f32618fa016be55eecf22
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In Geometry and Topology
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- Hailong Dao
- Osamu Iyama
- Charles Vial
- B. Keller
- Peter Jørgensen
- Gustavo Jasso
- I. Reiten
In Mathematical Physics
- Hailong Dao
- Ryo Takahashi
- Charles Vial
- Osamu Iyama
- Gustavo Jasso
- I. Reiten
- Peter Jørgensen
- B. Keller
Citations in the corpus
- Non-commutative resolutions of quotient singularities for reductive groups (2015, unknown): “1 [15,40,60,63] Assume that S is a normal noetherian domain.”
- Non-commutative resolutions and Grothendieck groups (2012, background): “v conjecture on the derived equivalence of birational Calabi-Yau varieties in dimension three. Van den Bergh’s work has quickly generated a sizable body of research, see for example the recent survey [20]. In this note we study a weaker notion which is called a non-commutative resolution (NCR). Defin”