Submission: 2009, Feb 6
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 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.
2000 Mathematics Subject Classification: 11E04, 16K20 (16W10)
Keywords and Phrases: Quadratic forms ; Algebras with involutions ; Clifford algebras ; Decomposability
Full text: dvi.gz 21 k, dvi 45 k, ps.gz 575 k, pdf.gz 128 k, pdf 144 k.