The Riemann-Hilbert Correspondence for Algebraic Stacks

TL;DR

This paper extends the classical Riemann-Hilbert correspondence to complex smooth algebraic stacks using infinity-category theory, establishing an equivalence between derived categories of D-modules and constructible sheaves.

Contribution

It introduces a novel infinity-categorical framework for the Riemann-Hilbert correspondence on algebraic stacks, generalizing prior results from schemes to stacks.

Findings

Constructed derived categories of D-modules and sheaves on algebraic stacks.

Established an infinity-categorical equivalence generalizing classical correspondence.

Provides a new foundation for studying D-modules and sheaves on stacks.

Abstract

Using the theory infinity-categories we construct derived (dg-)categories of regular, holonomic D-modules and algebraically constructible sheaves on a complex smooth algebraic stack. We construct a natural infinity-categorical equivalence between these two categories generalising the classical Riemann-Hilbert correspondence.