Families of rationally simply connected varieties over surfaces and torsors for semisimple groups
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- de Jong, A.J., He, X. & Starr, J.M. Publ.math.IHES (2011) 114: 1. doi:10.1007/s10240-011-0035-1
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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.