I. Panin, K. Pimenov: Rationally trivial quadratic spaces are locally trivial:III

paniniv@gmail.com, kip302002@yahoo.com

Submission: 2013, Feb 19

It is proved the following. Let R be a regular semi-local domain containing a field such that all the residue fields are infinite. Let K be the fraction field of R. If a quadratic space q over R is isotropic over K, then there is a unimodular vector v such that q(v)=0. If char(R)=2, then in the case of even n we assume that q is a non-singular space and in the case of odd n>2 we assume that R is a semi-regular qudratic space.

2010 Mathematics Subject Classification: 11E08

Keywords and Phrases: Isotropic quadratic space, semi-regular quadratic form

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