Birational invariance of the $S$-fundamental group scheme

TL;DR

This paper proves that the $S$-fundamental group scheme remains invariant under birational equivalence for nonsingular projective varieties over an algebraically closed field of positive characteristic.

Contribution

It establishes the birational invariance of the $S$-fundamental group scheme for a broad class of algebraic varieties in positive characteristic.

Findings

$S$-fundamental group schemes are isomorphic for birational varieties

Invariance holds over algebraically closed fields of positive characteristic

Extends understanding of fundamental group schemes in algebraic geometry

Abstract

Let $X$ and $Y$ be nonsingular projective varieties over an algebraically closed field $k$ of positive characteristic. If $X$ and $Y$ are birational, we show their $S$-fundamental group schemes are isomorphic.