Families of rationally simply connected varieties over surfaces and torsors for semisimple groups
Jong, A. J.1 ; He, Xuhua2 ; Starr, Jason Michael3
1 Department of Mathematics, Columbia University New York, NY, 10027 USA
2 Department of Mathematics, The Hong Kong University of Science and Technology Clear Water Bay, Kowloon Hong Kong
3 Department of Mathematics, Stony Brook University Stony Brook, NY, 11794 USA
Publications Mathématiques de l'IHÉS, Tome 114 (2011), pp. 1-85.

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.

DOI : 10.1007/s10240-011-0035-1
Jong, A. J. 1 ; He, Xuhua 2 ; Starr, Jason Michael 3

1 Department of Mathematics, Columbia University New York, NY, 10027 USA
2 Department of Mathematics, The Hong Kong University of Science and Technology Clear Water Bay, Kowloon Hong Kong
3 Department of Mathematics, Stony Brook University Stony Brook, NY, 11794 USA 
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Jong, A. J.; He, Xuhua; Starr, Jason Michael. Families of rationally simply connected varieties over surfaces and torsors for semisimple groups. Publications Mathématiques de l'IHÉS, Tome 114 (2011), pp. 1-85. doi : 10.1007/s10240-011-0035-1. http://www.numdam.org/articles/10.1007/s10240-011-0035-1/

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