Derived equivalence for quantum symplectic resolutions

Author: 

McGerty, K
Nevins, T

Publication Date: 

1 January 2014

Journal: 

Selecta Mathematica, New Series

Last Updated: 

2019-04-22T07:59:23.97+01:00

Issue: 

2

Volume: 

20

DOI: 

10.1007/s00029-013-0142-6

page: 

675-717

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. © 2013 Springer Basel.

Symplectic id: 

460134

Submitted to ORA: 

Not Submitted

Publication Type: 

Journal Article