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

  • A. J. de JongEmail author
  • Xuhua He
  • Jason Michael Starr


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.


Irreducible Component Rational Curf Linear Algebraic Group Cartier Divisor Invertible Sheaf 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


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Copyright information

© IHES and Springer-Verlag 2011

Authors and Affiliations

  • A. J. de Jong
    • 1
    Email author
  • 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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