Simply connected varieties in characteristic $p>0$
  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. 
H\'el\`ene Esnault and Vasudevan Srinivas (with an appendix by   Jean-Beno\^it Bost)
math.AG