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We present a simple proof of a strengthening of the derivedBeilinson-Bernstein localization theorem using the formalism of descent inderived algebraic geometry. The arguments and results apply to arbitrarymodules without the need to fix infinitesimal character. Roughly speaking, wedemonstrate that all Ug-modules are the invariants, or equivalentlycoinvariants, of the action of intertwining functors (a refined form of Weylgroup symmetry). This is a quantum version of descent for theGrothendieck-Springer simultaneous resolution. In an appendix we present analternative perspective, which identifies the descent data in both classicaland quantum versions as a categorical action of Demazure operators.

Beilinson-Bernstein localization over the Harish-Chandra center