Semifinite Bundles and the Chevalley-Weil Formula

TL;DR

This paper explores the structure of semifinite bundles on algebraic curves, demonstrating how the Chevalley-Weil formula describes the module structure of the fundamental group actions in characteristic zero.

Contribution

It provides an explicit module structure description of the fundamental group action using the Chevalley-Weil formula, building on previous work on semifinite bundles.

Findings

Chevalley-Weil formula describes the module structure

Faithful action of Nori fundamental group on unipotent fundamental group

Explicit description of fundamental group actions in characteristic zero

Abstract

In our previous paper, we studied the category of semifinite bundles on a proper variety defined over a field of characteristic 0. As a result, we obtained the fact that for a smooth projective curve defined over an algebraically closed field of characteristic 0 with genus $g>1$, Nori fundamental group acts faithfully on the unipotent fundamental group of its universal covering. However, it was not mentioned about any explicit module structure. In this paper, we prove that the Chevalley-Weil formula gives a description of it.