Prolongation of regular singular connections on punctured affine line over a Henselian ring

TL;DR

This paper extends Deligne's equivalence of categories for regular-singular connections from the punctured affine line to the case over a Henselian ring, including higher-dimensional bases, broadening the theoretical framework in algebraic geometry.

Contribution

It generalizes Deligne's equivalence to Henselian rings and explores the case of higher-dimensional bases, expanding the applicability of the theory.

Findings

Established equivalence over strictly Henselian discrete valuation rings

Extended results to higher-dimensional base schemes

Provided new insights into regular-singular connections over complex bases

Abstract

We generalize Deligne's equivalence between the categories of regular-singular connections on the formal punctured disk and on the punctured affine line to the case where the base is a strictly Henselian discrete valuation ring of equal characteristic 0. We also provide a weaker result when the base is higher dimensional.