Geodesic
A~normal form and schemes of quadratic forms
Fundamentalʹnaâ i prikladnaâ matematika, Tome 13 (2007) no. 1, pp. 161-178.

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We present a solution of the problem of the construction of a normal diagonal form for quadratic forms over a local principal ideal ring $R=2R$ with a QF-scheme of order 2. We give a combinatorial representation for the number of classes of projective congruence quadrics of the projective space over $R$ with nilpotent maximal ideal. For the projective planes, the enumeration of quadrics up to projective equivalence is given; we also consider the projective planes over rings with nonprincipal maximal ideal. We consider the normal form of quadratic forms over the field of $p$-adic numbers. The corresponding QF-schemes have order 4 or 8. Some open problems for QF-schemes are mentioned. The distinguished finite QF-schemes of local and elementary types (of arbitrarily large order) are realized as the QF-schemes of a field. 
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V. M. Levchuk; O. A. Starikova. A~normal form and schemes of quadratic forms. Fundamentalʹnaâ i prikladnaâ matematika, Tome 13 (2007) no. 1, pp. 161-178. http://geodesic.mathdoc.fr/item/FPM_2007_13_1_a8/

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