Regularity of a D-Module along a submanifold

TL;DR

This paper investigates how the regularity of D-modules along submanifolds propagates, establishing conditions under which regularity along a foliation implies regularity along individual submanifolds.

Contribution

It provides new criteria for the propagation of regularity of D-modules from foliations to submanifolds, linking regularity to characteristic variety conditions.

Findings

Regularity along a lagrangian foliation implies regularity of the system.

Regularity along a submanifold depends on characteristic variety conditions.

Propagation of regularity is characterized under specific geometric conditions.

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.