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GAGA for DQ-algebroid. (English) Zbl 1195.18004

Summary: Let \(X\) be a smooth complex projective variety with associated compact complex manifold \(X_{\text{an}}\). If \({\mathcal A}_X\) is a DQ-algebroid on \(X\), then there is an induced DQ-algebroid \({\mathcal A}_{X_{\text{an}}}\) on \(X_{\text{an}}\). We show that the natural functor from the derived category of bounded complexes of \({\mathcal A}_X\)-modules with coherent cohomologies to the derived category of bounded complexes of \({\mathcal A}_{X_{\text{an}}}\)-modules with coherent cohomologies is an equivalence.

MSC:

18E30 Derived categories, triangulated categories (MSC2010)
18D05 Double categories, \(2\)-categories, bicategories and generalizations (MSC2010)
32C38 Sheaves of differential operators and their modules, \(D\)-modules
46L65 Quantizations, deformations for selfadjoint operator algebras
53D55 Deformation quantization, star products
18F20 Presheaves and sheaves, stacks, descent conditions (category-theoretic aspects)
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