Quadratic forms of dimension 8 with trivial discrimiand and Clifford algebra of index 4

Details Quadratic forms of dimension 8 with trivial discrimiand and Clifford algebra of index 4 Quadratic forms of dimension 8 with trivial discrimiand and Clifford algebra of index 4

2009-02-06

arxiv.org/abs/0902.1031v1

Mathematics

Rings and Algebras

Scientific paper

Izhboldin and Karpenko proved in 2000 that any quadratic form of dimension 8 with trivial discriminant and Clifford algebra of index 4 is isometric to the transfer, with respect to some quadratic \'etale extension, of a quadratic form similar to a 2-fold Pfister form. We give a new proof of this result, based on a theorem of decomposability for degree 8 and index 4 algebras with orthogonal involution.

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