On hermitian Pfister forms

Abstract : 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.
Document type :
Journal articles
Journal of Algebra and Its Applications, World Scientific Publishing, 2008, 07 (05), pp.629-645. 〈10.1142/S021949880800303X〉
Liste complète des métadonnées

Cited literature [21 references]  Display  Hide  Download

https://hal.archives-ouvertes.fr/hal-01720724
Contributor : Nicolas Grenier-Boley <>
Submitted on : Thursday, March 1, 2018 - 2:59:53 PM
Last modification on : Thursday, November 15, 2018 - 8:27:32 PM
Document(s) archivé(s) le : Wednesday, May 30, 2018 - 1:41:34 PM

File

download-2-17.pdf
Files produced by the author(s)

Identifiers

Citation

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

Share

Metrics

Record views

73

Files downloads

35