DOCUMENTA MATHEMATICA, Quadratic Forms LSU (2001), 219-240

Ahmed Laghribi

Certaines Combinaisons Linéaires de Deux Formes de Pfister et le Problème d'Isotropie

In this paper we treat the isotropy problem of certain linear combinations of two Pfister forms over the function field of a projective quadric. More precisely, we discuss the connection between this problem and some conjectures on a field that appears in the generic splitting tower of a quadratic form associated to a given linear combination. The case of some linear combinations of low dimension will be detailed.

2000 Mathematics Subject Classification: 11E04, 11E81.

Keywords and Phrases: Forme quadratique, Forme de Pfister, Quadrique projective, D\'eploiement g\'en\'erique d'une forme quadratique, Cohomologie galoisienne.

Full text: dvi.gz 39 k, dvi 109 k, ps.gz 196 k, pdf 205 k.