panin at pdmi.ras.ru, victorapetrov at googlemail.com, a_stavrova at mail.ru

Submission: 2009, May 9

Assume that R is a semi-local regular ring containing an infinite perfect field, or that R is a semi-local ring of several points on a smooth scheme over an infinite field. Let K be the field of fractions of R. Let H be a strongly inner adjoint simple algebraic group of type E_6 or E_7 over R. We prove that under the above assumptions every principal H-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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