An Upper Bound for the Characteristic Variety of an Induced $\mathcal{D}$-Module

Abstract

We generalise the ${\text{Car}}_Y^Z(\mathfrak{M})$ upper bound of Laurent & Schapira [LS87] for the characteristic variety of the induced system of a coherent ${\mathcal{D}}_x$-module $\mathfrak{M}$ on a hypersurface $Y$ of $X$ to the case where $Y$ is a smooth submanifold of $X$ of arbitrary codimension.