A criterion for the existence of logarithmic connections on curves over a perfect field

TL;DR

This paper establishes a criterion for when vector bundles on smooth projective curves over perfect fields admit logarithmic connections with specified rigid residues, advancing understanding of connections in algebraic geometry.

Contribution

It provides a new criterion for the existence of logarithmic connections with prescribed residues on vector bundles over curves in characteristic zero.

Findings

Criterion for existence of logarithmic connections with rigid residues

Applicable to vector bundles over smooth projective curves

Advances understanding of connections in algebraic geometry

Abstract

Let $k$ be a perfect field, and $X$ an irreducible smooth projective curve over $k$. We give a criterion for a vector bundle over $X$ to admit a logarithmic connection singular over a finite subset of $X$ with given residues, where residues are assumed to be rigid.