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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
- 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)

- 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)

- 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)

- Pierre Schapira
- 2006

The aim of these Notes is to introduce the reader to the language of categories with emphazis on homological algebra. We treat with some details basic homological algebra, that is, categories of complexes in additive and abelian categories and construct with some care the derived functors. We also introduce the reader to the more sophisticated concepts of… (More)