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Autour des formes quadratiques quasi-voisines

Ahmed Laghribi

In this article we study a generalization of the notion of\break Pfister neighbors. An anisotropic quadratic form $\phi$ over a field $F$ of characteristic not $2$ is called a quasi-Pfister neighbor when the anisotropic part $(\phi_{F(\phi)})_{\an}$ is $F(\phi)$-similar to an $F$-quadratic form $\psi$ where $F(\phi)$ denotes the function field of the projective quadric given by $\phi$. We prove the uniqueness of $\psi$ up to $F$-similarity for forms $\phi$ of dimension $\leq 8$, odd dimension and many others of large dimension, and in these cases we give a precise description of $\psi$.

Homology, Homotopy and Applications, Vol. 6(2004), No. 1, pp. 5-16

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