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

Autor: de Jong, A. J., He, Xuhua, Starr, Jason Michael
Rok vydání: 2008
Předmět:
Druh dokumentu: Working Paper
Popis: 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.
Databáze: arXiv