Witt kernels of function field extensions in characteristic 2
Witt kernels of function field extensions in characteristic 2
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特征2中函数域扩展的Witt核
DOI：
10.1016/j.jpaa.2004.12.005
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发表时间：
2005
影响因子：
0.8
通讯作者：
Ahmed Laghribi
中科院分区：
文献类型：
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作者：
Ahmed Laghribi
在特征 2 中，我们给出了各向异性对称双线性形式的完整表征，这些双线性形式在二次形式的函数域上进行了代谢。我们还通过推广 Fitzgerald 的一些结果来研究此类域上非奇异二次型的双曲性 (Pacific J. Math. 109 (1983) 89)。作为一个应用，我们引入并研究了双线性形式的 Pfister 邻域概念，并对高度为 1 的各向异性双线性形式进行分类，即那些在其自身功能域上发生代谢的双线性形式。还包括其他后果。
In characteristic 2 we give a complete characterization of anisotropic symmetric bilinear forms that become metabolic over the function field of a quadratic form. We also study the hyperbolicity of nonsingular quadratic forms over such a field by generalizing some results by Fitzgerald (Pacific J. Math. 109 (1983) 89). As an application, we introduce and study the notion of Pfister neighbors for bilinear forms, and classify anisotropic bilinear forms of height 1, i.e. those that become metabolic over their own function fields. Other consequences are also included.