Derived equivalence for quantum symplectic resolutions

Details Derived equivalence for quantum symplectic resolutions Derived equivalence for quantum symplectic resolutions

2011-08-31

arxiv.org/abs/1108.6267v1

Mathematics

Algebraic Geometry

Scientific paper

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.

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