Geodesic
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

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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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     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},
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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

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