Rationally Isotropic Exceptional Projective Homogeneous Varieties Are Locally Isotropic

Assume that $R$ is a regular local ring that contains an infinite field and whose field of fractions $K$ has charactertistic $\ne 2$. Let $X$ be an exceptional projective homogeneous scheme over $R$. We prove that in most cases the condition $X(K)\neq\emptyset$ implies $X(R)\neq\emptyset$.

2010 Mathematics Subject Classification: 14M17, 20G35

Keywords and Phrases: projective homogeneous varieties, rational points, exceptional groups

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