Quadratic forms of dimension 8 with trivial discriminant and Clifford algebra of index 4
(2009) Archiv der Mathematik — Vol. 93, n° 2, p. 129-138 (2009)
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- Abstract
- Izhboldin and Karpenko proved in Math. Z. (234 (2000), 647-695, Theorem 16.10) 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 two-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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Masquelein, A., Quéguiner-Mathieu, A., & Tignol, J.-P. (2009). Quadratic forms of dimension 8 with trivial discriminant and Clifford algebra of index 4. Archiv der Mathematik, 93(2), 129-138. https://doi.org/10.1007/s00013-009-0019-2 (Original work published 2009)