Rationally isotropic quadratic spaces are locally isotropic. III
Rationally isotropic quadratic spaces are locally isotropic. III
Let $R$ be a regular semilocal domain containing a field such that all the residue fields are infinite. Let $K$ be the fraction field of $R$. Let $(R^n,q\colon R^n \to R)$ be a quadratic space over $R$ such that the quadric $\{q=0\}$ is smooth over $R$. If the quadratic space …