Vanishing in Highest Degree for Solutions of <I>D</I>-Modules and Perverse Sheaves

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  • Vanishing in Highest Degree for Solutions of $D$-Modules and Perverse Sheaves

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Let M be a real analytic manifold of dimension n, X a complexification of M, \mathscr{M} a coherent module over the sheaf of rings \mathscr{E}X of microdifferential operators. We prove the vanishing of the group \mathscr{E}xt\mathscr{E}<SUB>X</SUB>n(\mathscr{M}, \mathscr{C}M), where \mathscr{C}M denotes the sheaf of Sato's microfunctions. The proof makes use of the duality of perverse sheaves.

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