Abstract
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.
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