Simply connected projective manifolds in characteristic $p>0$ have no nontrivial stratified bundles

TL;DR

This paper proves that simply connected projective manifolds over fields of characteristic p>0 do not admit nontrivial stratified bundles, confirming a conjecture by Gieseker using Hrushovski's theorem.

Contribution

It establishes a significant result confirming Gieseker's conjecture for simply connected projective manifolds in positive characteristic.

Findings

Simply connected projective manifolds have no nontrivial stratified bundles

Confirms Gieseker's conjecture in characteristic p>0

Uses Hrushovski's theorem on periodic points

Abstract

We show that simply connected projective manifolds in characteristic $p>0$ have no nontrivial stratified bundles. This gives a positive answer to a conjecture by D. Gieseker. The proof uses Hrushovski's theorem on periodic points.