Derived equivalence for quantum symplectic resolutions
By Kevin McGerty, T. Nevins. 2011
47 citations recorded by the source corpus.
Using techniques from the homotopy theory of derived categories and noncommutative algebraic geometry, we establish a general theory of derived microlocalization for quantum symplectic resolutions. In particular, our results yield a new proof of derived Beilinson–Bernstein localization and a derived version of the more recent microlocalization theorems of Gordon–Stafford (Gordon and Stafford in Adv Math 198(1):222–274, 2005; Duke Math J 132(1):73–135, 2006) and Kashiwara–Rouquier (Kashiwara and Rouquier in Duke Math J 144(3):525–573, 2008) as special cases. We also deduce a new derived microlocalization result linking cyclotomic rational Cherednik algebras with quantized Hilbert schemes of points on minimal resolutions of cyclic quotient singularities.
Subfields: Algebra and Number Theory, Geometry and Topology, Mathematical Physics
View Paper: https://www.semanticscholar.org/paper/f1d82f9687558e4299cb1f9b6204fa0f4414423f
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In Algebra and Number Theory
In Geometry and Topology
- I. Losev
- I. Gordon
- Ben Webster
- Tom Braden
- Nicholas Proudfoot
- V. Ginzburg
- Pavel Etingof
- Stephen Griffeth
In Mathematical Physics
- I. Losev
- I. Gordon
- Ben Webster
- Tom Braden
- Nicholas Proudfoot
- V. Ginzburg
- Pavel Etingof
- Stephen Griffeth
Citations in the corpus
- On category O for cyclotomic rational Cherednik algebras (2011, methodology): “Our methods are complementary to the derived equivalences for Hp-mod of [48]: the latter are constructed for a general class of hamiltonian reductions but would, in the instance of this paper, require the parameters to be spherical.”
- Quantizations of conical symplectic resolutions I: local and global structure (2012, methodology): “les in a single coherent theory. Kashiwara and Rouquier began to develop such a theory [KR08], and our paper might be regarded as a continuation of their work. A recent preprint of McGerty and Nevins [MNa] addresses similar issues, with results that are complementary to ours. In Section 2, we discus”