Notes on regular holonomic $D$-modules for algebraic geometers

TL;DR

This paper introduces a formalism for regular holonomic D-modules tailored for algebraic geometers, utilizing algebraic local cohomology, Deligne extensions, and duality to deepen understanding.

Contribution

It develops a new formalism connecting regular holonomic D-modules with algebraic local cohomology and Deligne extensions, enhancing algebraic geometers' toolkit.

Findings

Formalism clarifies the structure of regular holonomic D-modules.

Connections established between local cohomology and D-module theory.

Framework facilitates further research in algebraic geometry and D-modules.

Abstract

We explain a formalism of regular holonomic $D$-modules for algebraic geometers using the distinguished triangles associated with algebraic local cohomology together with meromorphic Deligne extensions of local systems as well as the dual functor.