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- P. Schapira
- AAECC
- 1995

We study the truncated microsupport SS k of sheaves on a real manifold. Applying our results to the case of F = RHom D (M , O), the complex of holomorphic solutions of a coherent D-module M , we show that SS k (F) is completely determined by the characteristic variety of M. As an application, we obtain an extension theorem for the sections of H j (F), j <… (More)

- Andrea D’Agnolo, Pierre Schapira
- 2006

Let Λ be a smooth Lagrangian submanifold of a complex symplectic manifold X. We construct twisted simple holonomic modules along Λ in the stack of deformation-quantization modules on X.

- Pierre Schapira
- 2009

Consider a ring K, a topological space X and a sheaf A on X of K[[]]-algebras. Assuming A-adically complete and without-torsion, we first show how to deduce a coherency theorem for complexes of A-modules from the corresponding property for complexes of A /A-modules. We apply this result to prove that, under a natural properness condition, the convolution of… (More)

- Pierre Schapira
- 2008

This paper is the continuation of [12]. We construct the Hochschild class for coherent modules over a deformation quantization algebroid on a complex Poisson manifold. We also define the convolution of Hochschild homologies, and prove that the Hochschild class of the con-volution of two coherent modules is the convolution of their Hochschild classes. We… (More)

- Giuseppe Dito, Pierre Schapira
- 2006

The cotangent bundle T * X to a complex manifold X is classically endowed with the sheaf of k-algebras W T * X of deformation quantization, where k := W {pt} is a subfield of C[[, −1 ]. Here, we construct a new sheaf of k-algebras W t T * X which contains W T * X as a subalgebra and an extra central parameter t. We give the symbol calculus for this algebra… (More)

Consider a complex symplectic manifold X and the algebroid stack W X of deformation-quantization. For two regular holonomic W X-modules L i (i = 0, 1) supported by smooth Lagrangian submanifolds, we prove that the complex RHom W X (L 1 , L 0) is perverse over the field W pt and dual to the complex RHom W X (L 0 , L 1).

Let X be a complex manifold, V a smooth involutive submani-fold of T * X, M a microdifferential system regular along V , and F an R-constructible sheaf on X. We study the complex of temperate microfunction solutions of M associated with F , that is, the complex RHom DX (M, T µhom(F, O X)). We give a bound to its micro-support and solve the Cauchy problem… (More)

We study modules over the algebroid stack W X of deformation quantization on a complex symplectic manifold X and recall some results: construction of an algebra for ⋆-products, existence of (twisted) simple modules along smooth Lagrangian submanifolds, perversity of the complex of solutions for regular holonomic W X-modules, finiteness and duality for the… (More)