Submission: 2009, Aug 25
We study structure properties of reductive group schemes defined over a local ring and splitting over its etale quadratic extension. As an application we prove Serre--Grothendieck conjecture on rationally trivial torsors over a local regular ring containing a field of characteristic 0 for group schemes of type $F_4$ with trivial $g_3$ invariant.
2000 Mathematics Subject Classification: 14L15, 20G10, 11E72
Keywords and Phrases: Linear algebraic group, exceptional groups, torsor, non-abelian cohomology, Pfister forms, purity conjecture
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