Regular holonomic D[[h]]-modules

TL;DR

This paper explores the category of regular holonomic modules over D[[h]], establishing the Riemann-Hilbert correspondence and analyzing the t-structure associated with h-torsion.

Contribution

It extends the theory of regular holonomic D-modules to include the formal parameter h, providing new insights into their categorical structure and correspondence.

Findings

Established the Riemann-Hilbert correspondence for D[[h]]-modules.

Analyzed the t-structure related to h-torsion.

Described the category of regular holonomic modules over D[[h]].

Abstract

We describe the category of regular holonomic modules over the ring D[[h]] of linear differential operators with a formal parameter h. In particular, we establish the Riemann-Hilbert correspondence and discuss the additional t-structure related to h-torsion.