The isotropy of quadratic forms of dimension <=8 over the function field of a quadric

Let F be a field of characteristic not 2 and phi be art anisotropic quadratic form over F of dimension 8 with trivial discriminant. We give a characterization of the quadratic forms psi such that phi becomes isotropic over the function field F(psi) of the projective quadric defined by the equation psi = 0. We deduce some consequences on the isotropy of quadratic form of dimension 7. For quadratic forms of dimension less than or equal to 6, this allows us to solve most of the cases not considered by Hoffmann [4] and to recover the known results on the isotropy of quadratic form of dimension 5 or 6. The proofs of the results announced in this Note will appear in [8], [9] and [10].