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Let R be a regular semilocal domain containing a field such that all the residue fields are infinite. Let K be the fraction field of R. Let (Rn, q: Rn → R) be a quadratic space over R such that the quadric (q = 0) is smooth over R. If the quadratic space (Rn, q: Rn → R) over R is isotropic over K, then there is a unimodular vector v ∈ Rn such that q(v) = 0. If char(R) = 2, then in the case of even n the assumption on q is equivalent to the fact that q is a nonsingular quadratic space and in the case of odd n > 2 this assumption on q is equivalent to the fact that q is a semiregular quadratic space.
Original language | English |
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Pages (from-to) | 1029-1034 |
Journal | St. Petersburg Mathematical Journal |
Volume | 27 |
Issue number | 6 |
DOIs | |
State | Published - 1 Jan 2016 |
ID: 36910171