Preconstructibility of tempered solutions of holonomic D-modules

TL;DR

This paper proves the preconstructibility of tempered holomorphic solutions of holonomic D-modules, establishing finiteness properties crucial for confirming a conjecture on their constructibility.

Contribution

It demonstrates the preconstructibility of these solutions, advancing the understanding of their finiteness and supporting a significant conjecture in the field.

Findings

Preconstructibility of tempered solutions proved

Finiteness on relatively compact subanalytic sets established

Supports conjecture on constructibility of these complexes

Abstract

In this paper we prove the preconstructibility of the complex of tempered holomorphic solutions of holonomic D-modules on complex analytic manifolds. This implies the finiteness of such complex on any relatively compact open subanalytic subset of a complex analytic manifold. Such a result is an essential step for proving a conjecture of M. Kashiwara and P. Schapira (2003) on the constructibility of such complex.