%0 Journal Article
%T Rationally trivial quadratic spaces are locally trivial:III
%A Ivan Panin
%A Konstantin Pimenov
%J Mathematics
%D 2013
%I arXiv
%X Let R be a regular semi-local domain containing a field such that all the residue fields are infinite. Let K be the fraction field of R. Let q be a quadratic space over R on a free rank n R-module P such that the projective quadric q=0 is smooth over R. It is proved that if the quadratic space q is isotropic over K, then there is a unimodular vector v in the free rank n R-module P such that q(v)=0. If characteristic of R is 2, then in the case of even n our assumption on q is equivalent to the one that q is a non-singular space in the sense of \cite{Kn} and in the case of odd n > 2 our assumption on q is equivalent to the one that q is a semi-regular in the sense of \cite{Kn}.
%U http://arxiv.org/abs/1302.4845v1