Vanishing in highest degree for solutions of D-modules and perverse sheaves
Let M be a real analytic manifold of dimension n, X a complexification of M, \({\mathcal D}_ x\) the sheaf of differential operators on X, \({\mathcal E}_ x\) the sheaf on \(T^*X\) of (finite order) microdifferential operators and \({\mathcal M}\) a coherent module over the sheaf of rings \({\mathcal E}_ x.\) The author proves the vanishing of \({\mathcal E}xt^ j_{{\mathcal E}_ x}({\mathcal M},{\mathcal C}_ M)\) for \(j\geq n\), where \({\mathcal C}_ M\) denotes the sheaf of Sato's microfunctions. In particular, he obtains for coherent \({\mathcal D}_ x\)-modules \({\mathcal M}\) that \({\mathcal E}xt^ j_{{\mathcal D}_ x}({\mathcal M},{\mathcal B}_ M)=0\) for \(j\geq n\), where \({\mathcal B}_ M\) is the sheaf of Sato's hyperfunctions.
scientific article; zbMATH DE number 4203329