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- P. Schapira
- AAECC
- 1995

Let X ←−<lb>f<lb>Z −→<lb>g<lb>Y be a correspondence of complex manifolds. We study integral transforms associated to kernels exp(φ), with φ meromor-<lb>phic on Z, acting on formal or moderate cohomologies. Our main application<lb>is the Laplace transform. In this case, X is the projective compactification of<lb>the vector space V ' Cn, Y is its dual space,… (More)

We study the truncated microsupport SSk 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 SSk(F ) is completely determined by the characteristic variety of M . As an application, we obtain an extension theorem for the sections of Hj(F ), j < d,… (More)

Let X be a complex manifold, V a smooth involutive submanifold 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 RHomDX (M, T μhom(F,OX)). We give a bound to its micro-support and solve the Cauchy problem under a… (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. Mathematics Subject Classification: 46L65, 14A20, 32C38

Consider a complex symplectic manifold X and the algebroid stack WX of deformation-quantization. For two regular holonomic WXmodules Li (i = 0, 1) supported by smooth Lagrangian submanifolds, we prove that the complex RHom WX (L1,L0) is perverse over the field Wpt and dual to the complex RHomWX(L0,L1).

We study modules over the algebroid stack WX 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 WX -modules, finiteness and duality for the… (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 convolution of two coherent modules is the convolution of their Hochschild classes. We… (More)

- Andrea D’Agnolo, Pierre Schapira
- 2004

Using the notion of subprincipal symbol, we give a necessary condition for the existence of twisted D-modules simple along a smooth involutive submanifold of the cotangent bundle to a complex manifold. As an application, we prove that there are no generalized massless field equations with non trivial twist on grassmannians, and in particular that the… (More)

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