P. Schapira

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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)
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)
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)
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)