Families of rationally simply connected varieties over surfaces and torsors for semisimple groups |
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| Authors: | A. J. de Jong Xuhua He Jason Michael Starr |
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| Affiliation: | 1.Department of Mathematics,Columbia University,New York,USA;2.Department of Mathematics,The Hong Kong University of Science and Technology,Clear Water Bay,Hong Kong;3.Department of Mathematics,Stony Brook University,Stony Brook,USA |
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| Abstract: | 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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