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arXiv · 0902.1031

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

Alexandre Masquelein·Anne Quéguiner-Mathieu·Jean-Pierre Tignol
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Abstract

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 étale 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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Alexandre Masquelein, Anne Quéguiner-Mathieu, Jean-Pierre Tignol. 2009-02-06. Quadratic forms of dimension 8 with trivial discrimiand and Clifford algebra of index 4. https://arxiv.org/abs/0902.1031

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