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• W2069724166 abstract "We present a solution of the problem of 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." @default.
• W2069724166 created "2016-06-24" @default.
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• W2069724166 date "2008-07-01" @default.
• W2069724166 modified "2023-09-25" @default.
• W2069724166 title "A normal form and schemes of quadratic forms" @default.
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• W2069724166 doi "https://doi.org/10.1007/s10958-008-9078-3" @default.
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