Regularity of a D-Module Along a Submanifold

Abstract

We study how regularity along a submanifold of a differential or microdifferential system can propagate from a family of submanifolds to another. The first result is that a microdifferential system regular along a Lagrangian foliation is regular. However, when restricted to a fixed submanifold the corresponding result is true only under a condition on the characteristic variety.