Compatibility of t-structures for quantum symplectic resolutions
Let W be a smooth complex quasiprojective variety with the action of a connected reductive group G. Adapting the stratification approach of Teleman to a microlocal context, we prove a vanishing theorem for the functor of G-invariant sections---i.e., of quantum Hamiltonian reduction---for G-equivaria...
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| Format: | Journal article |
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Duke University Press
2016
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| _version_ | 1826259968577241088 |
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| author | McGerty, K Nevins, T |
| author_facet | McGerty, K Nevins, T |
| author_sort | McGerty, K |
| collection | OXFORD |
| description | Let W be a smooth complex quasiprojective variety with the action of a connected reductive group G. Adapting the stratification approach of Teleman to a microlocal context, we prove a vanishing theorem for the functor of G-invariant sections---i.e., of quantum Hamiltonian reduction---for G-equivariant twisted D-modules on W. As a consequence, when W is affine we establish an effective combinatorial criterion for exactness of the global sections functors of microlocalization theory. When combined with our earlier derived equivalence results, this gives precise criteria for "microlocalization of representation categories." |
| first_indexed | 2024-03-06T18:58:12Z |
| format | Journal article |
| id | oxford-uuid:129a301c-6162-49e3-b686-a001fea83e3e |
| institution | University of Oxford |
| last_indexed | 2024-03-06T18:58:12Z |
| publishDate | 2016 |
| publisher | Duke University Press |
| record_format | dspace |
| spelling | oxford-uuid:129a301c-6162-49e3-b686-a001fea83e3e2022-03-26T10:08:52ZCompatibility of t-structures for quantum symplectic resolutionsJournal articlehttp://purl.org/coar/resource_type/c_dcae04bcuuid:129a301c-6162-49e3-b686-a001fea83e3eSymplectic Elements at OxfordDuke University Press2016McGerty, KNevins, TLet W be a smooth complex quasiprojective variety with the action of a connected reductive group G. Adapting the stratification approach of Teleman to a microlocal context, we prove a vanishing theorem for the functor of G-invariant sections---i.e., of quantum Hamiltonian reduction---for G-equivariant twisted D-modules on W. As a consequence, when W is affine we establish an effective combinatorial criterion for exactness of the global sections functors of microlocalization theory. When combined with our earlier derived equivalence results, this gives precise criteria for "microlocalization of representation categories." |
| spellingShingle | McGerty, K Nevins, T Compatibility of t-structures for quantum symplectic resolutions |
| title | Compatibility of t-structures for quantum symplectic resolutions |
| title_full | Compatibility of t-structures for quantum symplectic resolutions |
| title_fullStr | Compatibility of t-structures for quantum symplectic resolutions |
| title_full_unstemmed | Compatibility of t-structures for quantum symplectic resolutions |
| title_short | Compatibility of t-structures for quantum symplectic resolutions |
| title_sort | compatibility of t structures for quantum symplectic resolutions |
| work_keys_str_mv | AT mcgertyk compatibilityoftstructuresforquantumsymplecticresolutions AT nevinst compatibilityoftstructuresforquantumsymplecticresolutions |