panin at pdmi.ras.ru, a_stavrova at mail.ru, nikolai-vavilov at yandex.ru
Submission: 2009, May 9
Let R be a semi-local regular domain containing an infinite perfect subfield and let K be its field of fractions. Let G be a reductive semi-simple simply connected R-group scheme such that each of its R-indecomposable factors is isotropic. We prove that under the above assumptions every principal G-bundle P which has a K-rational point is itself trivial. This confirms a conjecture posed by Serre and Grothendieck.
2000 Mathematics Subject Classification: 11E72; 14L17
Keywords and Phrases: reductive algebraic group, principal G-bundle, Grothendieck-Serre's conjecture
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