Isotropy of quadratic forms over the function field of a quadric in characteristic 2

JOURNAL OF ALGEBRA

卷:295

Article

Hoffmann, DW ; Laghribi, A

关键词: quadratic forms;    function field of a quadratic form;    Pfister forms;    Pfister neighbors;    dominated quadratic forms;    standard splitting of a quadratic form;    maximal splitting;   

DOI  :  10.1016/j.jalgebra.2004.02.038

来源: Elsevier

【 摘 要 】

We extend to characteristic 2 a theorem by the first author which states that if phi and psi are anisotropic quadratic forms over a field F such that dim phi <= 2 '' < dim psi for some nonnegative integer n, then phi stays anisotropic over the function field F(psi) of psi. The case of singular forms is systematically included. We give applications to the characterization of quadratic forms with maximal splitting. We also prove a characteristic 2 version of a theorem by Izhboldin on the isotropy of (p over F(psi) in the case dim phi = 2 '' + 1 <= dim psi. (c) 2005 Elsevier Inc. All rights reserved.

【 授权许可】

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