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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)
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)
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)
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)