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

2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/218919Izhboldin 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.Rings and Algebras11E04, 16K20, 16W10Quadratic forms of dimension 8 with trivial discrimiand and Clifford algebra of index 4text