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

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

2008-09-30

arxiv.org/abs/0809.5224v1

Mathematics

Algebraic Geometry

Scientific paper

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.

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