Duke Mathematical Journal

Compatibility of t-structures for quantum symplectic resolutions

Kevin McGerty and Thomas Nevins

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Let W be a smooth complex variety with the action of a connected reductive group G. Adapting Teleman’s stratification approach to a microlocal context, we prove a vanishing theorem for the functor of G-invariant sections—that is, of quantum Hamiltonian reduction—for G-equivariant twisted D-modules on W. As a consequence, when W is affine we establish a sufficient combinatorial condition for exactness of the global sections functors of microlocalization theory. When combined with the derived equivalence results of our recent work, this gives precise criteria for “microlocalization of representation categories” in the spirit of Kashiwara–Rouquier and many other authors.

Article information

Duke Math. J., Volume 165, Number 13 (2016), 2529-2585.

Received: 21 March 2014
Revised: 16 October 2015
First available in Project Euclid: 23 June 2016

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Zentralblatt MATH identifier

Primary: 16G99: None of the above, but in this section
Secondary: 53D55: Deformation quantization, star products 53D20: Momentum maps; symplectic reduction 17B63: Poisson algebras 16S38: Rings arising from non-commutative algebraic geometry [See also 14A22]

quantum Hamiltonian reduction $D$-modules microlocalization $t$-exactness localization Kirwan–Ness stratification


McGerty, Kevin; Nevins, Thomas. Compatibility of $t$ -structures for quantum symplectic resolutions. Duke Math. J. 165 (2016), no. 13, 2529--2585. doi:10.1215/00127094-3619684. https://projecteuclid.org/euclid.dmj/1466703957

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