Geodesic
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
Documenta mathematica, Andrei A. Suslin's Sixtieth Birthday (2010), pp. 147-169.

Voir la notice de l'article provenant de la source Electronic Library of Mathematics

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.
Classification : 14L15, 20G10, 20G15
Keywords: linear algebraic groups, exceptional groups, torsors, non-Abelian cohomology, local regular rings, Grothendieck-Serre conjecture 
@article{DOCMA_2010__S4__a17,
     author = {Chernousov, V.},
     title = {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},
     journal = {Documenta mathematica},
     pages = {147--169},
     publisher = {mathdoc},
     volume = {Andrei A. Suslin's Sixtieth Birthday},
     year = {2010},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/DOCMA_2010__S4__a17/}
}
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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. Documenta mathematica, Andrei A. Suslin's Sixtieth Birthday (2010), pp. 147-169. http://geodesic.mathdoc.fr/item/DOCMA_2010__S4__a17/