Families of rationally simply connected varieties over surfaces and torsors for semisimple groups

de Jong, A. J.; He, Xuhua; Starr, Jason Michael

Families of rationally simply connected varieties over surfaces and torsors for semisimple groups

Authors

de Jong, A. J.

He, Xuhua

Starr, Jason Michael

Description

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.