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

Authors
  • de Jong, A. J.
  • He, Xuhua
  • Starr, Jason Michael
Type
Preprint
Publication Date
Sep 30, 2008
Submission Date
Sep 30, 2008
Identifiers
arXiv ID: 0809.5224
Source
arXiv
License
Yellow
External links

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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