A formula for Gau{\ss}-Manin determinants

TL;DR

This paper provides an explicit formula for the determinant of the Gau{ ext{-}}Manin connection associated with irregular connections on open subsets of the projective line over a function field.

Contribution

It introduces a new explicit formula for Gau{ ext{-}}Manin determinants in the context of irregular connections on algebraic curves.

Findings

Explicit formula for Gau{ ext{-}}Manin determinants

Applicable to irregular connections on $ ext{P}^1_K$

Advances understanding of algebraic connections and their determinants

Abstract

We give an explicit formula for the determinant of the Gau{\ss}-Manin connection for an irregular connection on a Zariski open set of the projective line $\P^1_K$ over a function field $K$ over a field $k$ of characteristic zero.