Truncated microsupport and hyperbolic inequalities

Details Truncated microsupport and hyperbolic inequalities Truncated microsupport and hyperbolic inequalities

2005-06-21

arxiv.org/abs/math/0506436v2

Mathematics

Algebraic Geometry

Corollary 1.8 is improved, corollary 1.9 is supressed, some minor changes of redaction

Scientific paper

We 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 $F=\text{R}\cal{H}\text{om}_{\cal{D}}(\cal{M}, \sho)$, where $\cal{M}$ is a coherent $\cal{D}$-module, we obtain new estimates for the truncated microsupport of real analytic and hyperfunction solutions. When $\cal{M}$ 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 $\shm$ when $Y$ is a hypersurface.

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