On the fundamental group schemes of certain quotient varieties

TL;DR

This paper extends Armstrong's classical theorem on fundamental groups to the setting of $F$-divided and essentially finite group schemes, broadening the understanding of quotient varieties in algebraic geometry.

Contribution

It provides an analogue of Armstrong's theorem for fundamental group schemes, a significant generalization in algebraic geometry.

Findings

Established an analogue of Armstrong's theorem for $F$-divided fundamental group schemes.

Extended classical results to the setting of essentially finite group schemes.

Enhanced understanding of the fundamental group schemes of quotient varieties.

Abstract

In \cite{armstrong}, M. Armstrong proved a beautiful result describing fundamental groups of quotient spaces. In this paper we prove an analogue of Armstrong's theorem in the setting of $F$-divided \cite{dS07} and essentially finite \cite{Nori76} fundamental group schemes.