Tilting and cluster tilting for quotient singularities
By Osamu Iyama, Ryo Takahashi. 2010
81 citations recorded by the source corpus.
We shall show that the stable categories of graded Cohen–Macaulay modules over quotient singularities have tilting objects. In particular, these categories are triangle equivalent to derived categories of finite dimensional algebras. Our method is based on higher dimensional Auslander–Reiten theory, which gives cluster tilting objects in the stable categories of (ungraded) Cohen–Macaulay modules.
Subfields: Algebra and Number Theory, Geometry and Topology, Statistical and Nonlinear Physics
View Paper: https://www.semanticscholar.org/paper/f81cab9d490ed22b35df2d82afd38462dcd039ef
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In Algebra and Number Theory
- Osamu Iyama
- I. Reiten
- C. Amiot
- B. Keller
- Peter Jørgensen
- Gustavo Jasso
- Steffen Oppermann
- Aslak Bakke Buan
In Geometry and Topology
- Osamu Iyama
- I. Reiten
- C. Amiot
- B. Keller
- Gustavo Jasso
- Peter Jørgensen
- Aslak Bakke Buan
- Bernard Leclerc
In Statistical and Nonlinear Physics
- Osamu Iyama
- I. Reiten
- C. Amiot
- B. Keller
- Bernard Leclerc
- Peter Jørgensen
- Gustavo Jasso
- Aslak Bakke Buan
Citations in the corpus
- Stable categories of Cohen-Macaulay modules and cluster categories: Dedicated to Ragnar-Olaf Buchweitz on the occasion of his sixtieth birthday (2011, result): “resting to generalize our result to non-cyclic quotient singularities. This could then be regarded as an analog of a triangle equivalence CMZ(SG) ≃ Db(Λ) for some finite dimensional algebra Λ given in [IT10]. Results of a similar flavor have been shown in previous papers. In [Ami09, ART11, AIRT12], it”