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

Alexandre Masquelein (1) , Anne Quéguiner-Mathieu (2) , Jean-Pierre Tignol (1)

1 Département de mathématique [Louvain]
2 LAGA - Laboratoire Analyse, Géométrie et Applications

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.

Mots clés: Quadratic forms; Algebras with involution

Domaines: Anneaux et algèbres [math.RA]

Alexandre Masquelein, Anne Quéguiner-Mathieu, Jean-Pierre Tignol. Quadratic forms of dimension $8$ with trivial discrimiand and Clifford algebra of index $4$.. 2009. ⟨hal-00359156⟩