Ivan Panin, Anastasia Stavrova, Nikolai Vavilov: On Grothendieck---Serre's conjecture concerning principal G-bundles over reductive group schemes: I

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

Full text: dvi.gz 63 k, dvi 194 k, ps.gz 853 k, pdf.gz 266 k, pdf 334 k.

Server Home Page