I. Panin: Rationally isotropic quadratic spaces are locally isotropic

panin@pdmi.ras.ru

Submission: 2003, Dec, 6

Let $R$ be a regular local ring, $K$ its field of fractions and $(V,\varphi)$ a quadratic space over R. In the case of $R$ containing a field of characteristic zero we show that if $(V,\varphi) \otimes_R K$ is isotropic over $K$, then $(V,\varphi)$ is isotropic over $R$.

2000 Mathematics Subject Classification: 11Exx