Generically isotropic reductive group schemes are locally isotropic

Abstract

Let $R$ be a semilocal geometrically factorial Noetherian domain of characteristic zero. We show that a reductive $R$-group scheme is isotropic if it is generically isotropic. We derive various consequences, in particular for the Grothenieck-Serre conjecture and for homotopic invariance of torsors.

Existence part of Proposition 3.13 is incorrect invalidating the argument