Categorical Cell Decomposition of Quantized Symplectic Algebraic Varieties
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arXiv
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| Auteurs principaux: | , , , |
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| Format: | Preprint |
| Publié: |
2013
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| _version_ | 1866913423447556096 |
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| author | Bellamy, Gwyn Dodd, Christopher McGerty, Kevin Nevins, Thomas |
| author_facet | Bellamy, Gwyn Dodd, Christopher McGerty, Kevin Nevins, Thomas |
| contents | We prove a new symplectic analogue of Kashiwara's Equivalence from D-module theory. As a consequence, we establish a structure theory for module categories over deformation quantizations that mirrors, at a higher categorical level, the Bialynicki-Birula stratification of a variety with an action of the multiplicative group. The resulting categorical cell decomposition provides an algebro-geometric parallel to the structure of Fukaya categories of Weinstein manifolds. From it, we derive concrete consequences for invariants such as K-theory and Hochschild homology of module categories of interest in geometric representation theory. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_1311_6804 |
| institution | arXiv |
| publishDate | 2013 |
| record_format | arxiv |
| spellingShingle | Categorical Cell Decomposition of Quantized Symplectic Algebraic Varieties Bellamy, Gwyn Dodd, Christopher McGerty, Kevin Nevins, Thomas Algebraic Geometry Quantum Algebra Symplectic Geometry We prove a new symplectic analogue of Kashiwara's Equivalence from D-module theory. As a consequence, we establish a structure theory for module categories over deformation quantizations that mirrors, at a higher categorical level, the Bialynicki-Birula stratification of a variety with an action of the multiplicative group. The resulting categorical cell decomposition provides an algebro-geometric parallel to the structure of Fukaya categories of Weinstein manifolds. From it, we derive concrete consequences for invariants such as K-theory and Hochschild homology of module categories of interest in geometric representation theory. |
| title | Categorical Cell Decomposition of Quantized Symplectic Algebraic Varieties |
| topic | Algebraic Geometry Quantum Algebra Symplectic Geometry |
| url | https://arxiv.org/abs/1311.6804 |