Geodesic
Rationally isotropic quadratic spaces are locally isotropic. II.
Documenta mathematica, Andrei A. Suslin's Sixtieth Birthday (2010), pp. 515-523.

Voir la notice de l'article provenant de la source Electronic Library of Mathematics

The results of the present article extend the results of [Zbl 1173.11025]. The main result of the article is Theorem 1.1 below. The proof is based on a moving lemma from [Zbl 1188.14015], a recent improvement due to O. Gabber of de Jong's alteration theorem, and the main theorem of [Zbl 1206.13008]. 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 [Zbl 0980.11025] and it is used to prove the main result in [Zbl 1126.14053].
Classification : 11E08, 11E81, 11E88, 13C10
Keywords: quadratic space, purity theorem, regular local ring 
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     author = {Panin, Ivan and Pimenov, Konstantin},
     title = {Rationally isotropic quadratic spaces are locally isotropic. {II.}},
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     volume = {Andrei A. Suslin's Sixtieth Birthday},
     year = {2010},
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Panin, Ivan; Pimenov, Konstantin. Rationally isotropic quadratic spaces are locally isotropic. II.. Documenta mathematica, Andrei A. Suslin's Sixtieth Birthday (2010), pp. 515-523. http://geodesic.mathdoc.fr/item/DOCMA_2010__S4__a6/