Simply connected varieties in characteristic $p>0$

Abstract

We show that there are no non-trivial stratified bundles over a smooth simply connected quasi-projective variety over the algebraic closure of a finite field, if the variety admits a normal projective compactification with boundary locus of codimension $\ge 2$. In the appendix, various strong forms of the Lefschetz LEF are proven. Final version, to appear in Compositio.

32 pages

References in corpus (4)

• Bertini theorems over finite fields
• Simply connected projective manifolds in characteristic $p>0$ have no nontrivial stratified bundles
• Analytic curves in algebraic varieties over number fields
• Gauss-Manin stratification and stratified fundamental group schemes

Cited by in corpus (1)

• On the fundamental group schemes of certain quotient varieties