%0 Journal Article
%T Families of rationally simply connected varieties over surfaces and torsors for semisimple groups
%A A. J. de Jong
%A Xuhua He
%A Jason Michael Starr
%J Mathematics
%D 2008
%I arXiv
%X Under suitable hypotheses, we prove that a form of a projective homogeneous variety $G/P$ defined over the function field of a surface over an algebraically closed field has a rational point. The method uses an algebro-geometric analogue of simple connectedness replacing the unit interval by the projective line. As a consequence, we complete the proof of Serre's Conjecture II in Galois cohomology for function fields over an algebraically closed field.
%U http://arxiv.org/abs/0809.5224v1