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


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

Full text: dvi.gz 43 k, dvi 102 k, ps.gz 703 k, pdf.gz 208 k, pdf 232 k.

Server Home Page