Algebraic connections vs. Algebraic $\mathcal D$-modules: regularity conditions

TL;DR

This paper compares the concepts of regularity in algebraic connections and algebraic -modules, highlighting their differences and similarities within the context of algebraic geometry.

Contribution

It provides a detailed analysis of the regularity conditions for algebraic connections and -modules, clarifying their relationship and distinctions.

Findings

Identifies key differences between regularity in algebraic connections and -modules.

Establishes criteria for regularity in both frameworks.

Provides insights into the implications for algebraic -module theory.

Abstract

This paper is devoted to the comparison of the notions of regularity for algebraic connections and (holonomic) regularity for algebraic $\mathcal D$-modules.