Categorical Cell Decomposition of Quantized Symplectic Algebraic Varieties

Abstract

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.

Version 3. Updated to agree with the version accepted for publication

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Cited by in corpus (3)

• Kirwan surjectivity for quiver varieties
• Very stable Higgs bundles, equivariant multiplicity and mirror symmetry
• Quantizations of multiplicative hypertoric varieties at a root of unity