Publications mathématiques de l'IHÉS

, Volume 114, Issue 1, pp 1–85 | Cite as

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



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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Copyright information

© IHES and Springer-Verlag 2011

Authors and Affiliations

  • A. J. de Jong
    • 1
  • Xuhua He
    • 2
  • Jason Michael Starr
    • 3
  1. 1.Department of MathematicsColumbia UniversityNew YorkUSA
  2. 2.Department of MathematicsThe Hong Kong University of Science and TechnologyClear Water BayHong Kong
  3. 3.Department of MathematicsStony Brook UniversityStony BrookUSA

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