A Riemann-Hilbert correspondence in positive characteristic

TL;DR

This paper develops a version of the Riemann-Hilbert correspondence tailored for p-torsion étale sheaves on schemes over finite fields, extending classical complex-analytic ideas to positive characteristic.

Contribution

It introduces a new Riemann-Hilbert correspondence framework for p-torsion étale sheaves in positive characteristic, broadening the scope of the classical theory.

Findings

Establishes a correspondence between p-torsion étale sheaves and certain algebraic structures.

Provides a new perspective on sheaf theory in positive characteristic.

Extends classical Riemann-Hilbert results to a broader algebraic setting.

Abstract

We explain a version of the Riemann-Hilbert correspondence for $p$-torsion \'etale sheaves on an arbitrary $\mathbf{F}_p$-scheme.