Derived equivalence for quantum symplectic resolutions

Kevin McGerty, Thomas Nevins

Research output: Contribution to journalArticle

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.

Original languageEnglish (US)
Pages (from-to)675-717
Number of pages43
JournalSelecta Mathematica, New Series
Volume20
Issue number2
DOIs
StatePublished - Jan 1 2014

Keywords

  • Derived equivalences
  • Microlocalization
  • Quantum Hamiltonian reduction

ASJC Scopus subject areas

  • Mathematics(all)
  • Physics and Astronomy(all)

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