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

V. Chernousov
Department of Mathematics University of Alberta Edmonton, Alberta T6G 2G1, Canada

Abstract

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.