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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DOI: 10.1007/s10240-011-0035-1
A. J. Jong 1; Xuhua He 2; Jason Michael Starr 3
@article{PMIHES_2011__114__1_0,
author = {A. J. Jong and Xuhua He and Jason Michael Starr},
title = {Families of rationally simply connected varieties over surfaces and torsors for semisimple groups},
journal = {Publications Math\'ematiques de l'IH\'ES},
pages = {1--85},
year = {2011},
publisher = {Springer-Verlag},
volume = {114},
doi = {10.1007/s10240-011-0035-1},
zbl = {1285.14053},
language = {en},
url = {https://pmihes.centre-mersenne.org/articles/10.1007/s10240-011-0035-1/}
}
TY - JOUR AU - A. J. Jong AU - Xuhua He AU - Jason Michael Starr TI - Families of rationally simply connected varieties over surfaces and torsors for semisimple groups JO - Publications Mathématiques de l'IHÉS PY - 2011 SP - 1 EP - 85 VL - 114 PB - Springer-Verlag UR - https://pmihes.centre-mersenne.org/articles/10.1007/s10240-011-0035-1/ DO - 10.1007/s10240-011-0035-1 LA - en ID - PMIHES_2011__114__1_0 ER -
%0 Journal Article %A A. J. Jong %A Xuhua He %A Jason Michael Starr %T Families of rationally simply connected varieties over surfaces and torsors for semisimple groups %J Publications Mathématiques de l'IHÉS %D 2011 %P 1-85 %V 114 %I Springer-Verlag %U https://pmihes.centre-mersenne.org/articles/10.1007/s10240-011-0035-1/ %R 10.1007/s10240-011-0035-1 %G en %F PMIHES_2011__114__1_0
A. J. Jong; Xuhua He; Jason Michael Starr. Families of rationally simply connected varieties over surfaces and torsors for semisimple groups. Publications Mathématiques de l'IHÉS, Volume 114 (2011), pp. 1-85. doi: 10.1007/s10240-011-0035-1
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