Deformation Quantization Modules

By Masaki Kashiwara, P. Schapira. 2010

104 citations recorded by the source corpus.

We study modules over stacks of deformation quantization algebroids on complex Poisson manifolds. We prove finiteness and duality theorems in the relative case and construct the Hochschild class of coherent modules. We prove that this class commutes with composition of kernels, a kind of Riemann-Roch theorem in the non-commutative setting. Finally we study holonomic modules on complex symplectic manifolds and we prove in particular a constructibility theorem.

Subfields: Algebra and Number Theory, Geometry and Topology, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/d42fe346e6543da6afda9d0185cd7ec111f2500d

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In Algebra and Number Theory

In Geometry and Topology

In Mathematical Physics

Citations in the corpus

Quantizations of conical symplectic resolutions I: local and global structure (2012, methodology): “laced by a subcategory CL ⊂D-mod (respectively CL0 ⊂A-mod) which is a module category for the category of geometric (respectively algebraic) Harish-Chandra bimodules. Following Kashiwara and Schapira [KS12], we deﬁne the characteristic cycle of a geometric HarishChandra bimodule, which lies in Z, an”
On the Homology of Completion and Torsion (2010, methodology): “ paper is to clarify the foundations of the theory in the algebraic setting. We also extend the scope of the existing results. Two other, much more recent papers also inﬂuenced our work. In the paper [KS2] of Kashiwara-Schapira there is a part devoted to what they call cohomologically complete compl”
Cohomologically Cofinite Complexes (2012, methodology): “This is influenced by the paper [8], as explained in Remark 2.”
Symmetries and stabilization for sheaves of vanishing cycles (2012, background): “(6.13) Observe that the work of Behrend–Fantechi and Kashiwara–Schapira cited above supports the existence of (6.12)–(6.13): there are natural products ExtkOS (K 1/2 L ,K 1/2 M )⊗OS Ext l OS (K 1/2 M ,K 1/2 N ) −→ Ext k+l OS (K 1/2 L ,K 1/2 N ), RH om(D•, E•) L ⊗RH om(E•,F•) −→ RH om(D•,F•).”