An Extension of Nori Fundamental Group

TL;DR

This paper explores an extension of Nori's fundamental group over characteristic 0 fields, establishing structure theorems and analyzing its action on unipotent bundles for curves of genus greater than or equal to 1.

Contribution

It introduces a new extension of Nori's fundamental group and provides detailed structure theorems, including its faithful action on unipotent bundles for certain algebraic curves.

Findings

Nori's fundamental group acts faithfully on unipotent bundles for genus > 1 curves.

Structure theorems for the extended fundamental group in characteristic 0.

Refined results for genus 1 curves.

Abstract

In this paper, we study a certain extension of Nori's fundamental group in the case where a base field is of characteristic 0 and give structure theorems about it. As a result, for a smooth projective curve with genus $g$>1, we prove that Nori's fundamental group acts faithfully on the category of unipotent bundles on the universal covering. In the case when $g=1$, we give a more finer result.