Quadratic forms of dimension $8$ with trivial discrimiand and Clifford algebra of index $4$.
Résumé
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.
Domaines
Anneaux et algèbres [math.RA]| Origine | Fichiers produits par l'(les) auteur(s) |
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