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

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.