The algebraic fundamental group of a reductive group scheme over an arbitrary base scheme

TL;DR

This paper introduces a new algebraic fundamental group functor for reductive group schemes over any base scheme and proves its exactness, extending the understanding of their algebraic structure.

Contribution

It defines the algebraic fundamental group functor for reductive group schemes over arbitrary bases and establishes its exactness, a significant theoretical advancement.

Findings

The functor is well-defined over arbitrary base schemes.

The algebraic fundamental group functor is proven to be exact.

This work generalizes previous results to broader contexts.

Abstract

We define the algebraic fundamental group functor of a reductive group scheme over an arbitrary (non-empty) base scheme and prove that this functor is exact.