Tensor product and irregularity for holonomic D-modules

TL;DR

This paper proves that for a complex of holonomic D-modules, regularity of its self-derived tensor product implies the regularity of the module itself, providing a criterion for regularity.

Contribution

It establishes a new criterion linking the regularity of a D-module to the regularity of its derived tensor product with itself.

Findings

Derived tensor product regularity implies module regularity

Provides a new approach to analyze D-module regularity

Advances understanding of holonomic D-module properties

Abstract

Let M be a complex of D-modules with bounded holonomic cohomology on a complex manifold. In this note, we prove that if the derived tensor product of M with itself is regular, then M is regular.