On hermitian Pfister forms

Nicolas Grenier-Boley (1) , Emmanuel Lequeu (2) , Mohammad Gholamzadeh Mahmoudi (3)

1 LDAR (EA_4434) - Laboratoire de Didactique André Revuz
2 ULR - La Rochelle Université
3 SUT - Sharif University of Technology [Tehran]

Let K be a field of characteristic different from 2. It is known that a quadratic Pfister form over K is hyperbolic once it is isotropic. It is also known that the dimension of an anisotropic quadratic form over K belonging to a given power of the fundamental ideal of the Witt ring of K is lower bounded. In this paper, weak analogues of these two statements are proved for hermitian forms over a multiquaternion algebra with invo-lution. Consequences for Pfister involutions are also drawn. An invariant uα of K with respect to a non-zero pure quaternion of a quaternion division algebra over K is defined. Upper bounds for this invariant are provided. In particular an analogue is obtained of a result of Elman and Lam concerning the u-invariant of a field of level at most 2.

Domaines: Mathématiques [math]

Nicolas Grenier-Boley, Emmanuel Lequeu, Mohammad Gholamzadeh Mahmoudi. On hermitian Pfister forms. Journal of Algebra and Its Applications, 2008, 07 (05), pp.629-645. ⟨10.1142/S021949880800303X⟩. ⟨hal-01720724⟩