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

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.

16 pages. Revised version contains a more general theorem on torsion points on moduli, together with an illustration in rank 2 due to M. Raynaud. Reference added. Last version has some typos corrected. Appears in Invent.math.

Cited by in corpus (4)

• On the S-fundamental group scheme II
• Nonvanishing for threefolds in characteristic $p>5$
• Simply connected varieties in characteristic $p>0$
• On smooth projective D-affine varieties