Rationally trivial quadratic spaces are locally trivial:III
نویسندگان
چکیده
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 (R, q : R → R) over R is isotropic over K, then there is a unimodular vector v ∈ R 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 in the sense of [Kn] and in the case of odd n > 2 we assume that q is a semi-regular in the sense of [Kn].
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