#### DOCUMENTA MATHEMATICA,
Vol. Extra Volume: Andrei A. Suslin's Sixtieth Birthday (2010), 515-523

** Ivan Panin and Konstantin Pimenov **
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:

Keywords and Phrases:

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