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Rationally isotropic exceptional projective homogeneous varieties are locally isotropic
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classification
math.AG
keywords
fieldexceptionalhomogeneousinfiniteisotropiclocalprojectivering
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Assume that R is a local regular ring containing an infinite perfect field, or that R is the local ring of a point on a smooth scheme over an infinite field. Let K be the field of fractions of R and the characteristic of K is not 2. Let X be an exceptional projective homogeneous scheme over R. We prove that in most cases the condition that X has a K-point implies that X has an R-point.
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