Truncated Microsupport and Hyperbolic Inequalities

Abstract

AbstractWe prove that the k-truncated microsupport of the specialization of a complex of sheaves F along a submanifold is contained in the normal cone to the conormal bundle along the k-truncated microsupport of F. In the complex case, applying our estimates to , where is a coherent -module, we obtain new estimates for the truncated microsupport of real analytic and hyperfunction solutions. When is regular along Y we also obtain estimates for the truncated microsupport of the holomorphic solutions of the induced system along Y as well as for the nearby-cycle sheaf of when Y is a hypersurface.