Chernousov, V.

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

Doc. Math. (Bielefeld) Extra Vol. Andrei A. Suslin's Sixtieth Birthday, 147-169 (2010)


We study structure properties of reductive group schemes defined over a local ring and splitting over its étale 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.

Mathematics Subject Classification

14L15, 20G10, 20G15


linear algebraic groups, exceptional groups, torsors, non-Abelian cohomology, local regular rings, Grothendieck-Serre conjecture