Derived equivalence for quantum symplectic resolutions

Journal article

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 and Kashiwara-Rouquier 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.

Authors: McGerty, K; Nevins, T

• Publication status: Published
• Journal: SELECTA MATHEMATICA-NEW SERIES
• Volume: 20
• Issue: 2
• Pages: 675-717
• Publication date: 2011-08-31
• DOI: 10.1007/s00029-013-0142-6
• EISSN: 1420-9020
• ISSN: 1022-1824
• Keywords: math.RT; math.AG; math.QA