Victor Petrov, Anastasia Stavrova: Grothendieck---Serre conjecture for groups of type F_4 with trivial f_3 invariant,

Submission: 2010, Jan 6

Assume that R is a semi-local regular ring containing an infinite perfect field. Let K be the field of fractions of R. Let H be a simple algebraic group of type F_4 over R such that H_K is the automorphism group of a 27-dimensional Jordan algebra which is a first Tits construction. If the characteristic of K is not 2 this means precisely that the f_3 invariant of H_K is trivial. We prove that under the above assumptions every principal H-bundle P which has a K-rational point is itself trivial. This complements the result of Chernousov on the Grothendieck-Serre conjecture for groups of type F_4 with trivial g_3 invariant.

2000 Mathematics Subject Classification: 11E72, 14L17, 17C40

Keywords and Phrases: reductive algebraic groups, principal G-bundle, Grothendieck-Serre's conjecture, exceptional Jordan algebras

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