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

2008/09/30 by A. J. de Jong, de Jong, A. J., Xuhua He +3 · 3 citations
Mathematics · #Advanced Algebra and Geometry #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #FOS: Mathematics #Geometric and Algebraic Topology

paper · pdf · doi:10.48550/arxiv.0809.5224

openalex publication_date 2008/09/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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.

Citations

• Resolution of Singularities of an Algebraic Variety Over a Field of Characteristic Zero: I

Cited by

• On the Problem of Mixed-Tateness of the Motives of G-Varieties
• Rationally Simply Connected Hypersurfaces in Orthogonal Grassmannians
• Homogeneous spaces over an abelian variety

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