Rationally Isotropic Quadratic Spaces Are Locally Isotropic: II

The results of the present article extend the results of [Pa]. The main result of the article is Theorem 1.1 below. The proof is based on a moving lemma from [LM], a recent improvement due to O. Gabber of de Jong's alteration theorem, and the main theorem of [PR]. A purity theorem for quadratic spaces is proved as well in the same generality as Theorem 1.1, provided that $R$ is local. It generalizes the main purity result from [OP] and it is used to prove the main result in [ChP].

2010 Mathematics Subject Classification:

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