Mélanie Raczek: On the 3-Pfister number of quadratic forms

melanie.raczek@uclouvain.be

Submission: 2010, Nov 23

For a field F of characteristic different from 2, containing a square root of -1, endowed with an F^{\times2}-compatible valuation v such that the residue field has at most two square classes, we use a combinatorial analogue of the Witt ring of F to prove that an anisotropic quadratic form over F with even dimension d, trivial discriminant and Hasse-Witt invariant can be written in the Witt ring as the sum of at most (d^2)/8 3-fold Pfister forms.

2000 Mathematics Subject Classification: 11E81

Keywords and Phrases: Algebraic theory of quadratic forms; Witt groups and rings

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