Vladimir Chernousov: Variations on a theme of groups splitting by a quadratic extension and Grothendieck-Serre conjecture for group schemes $F_4$ with trivial $g_3$ invariant

chernous@math.ualberta.ca

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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