Root numbers of elliptic curves in residue characteristic 2
Root numbers of elliptic curves in residue characteristic 2
复制标题
留数特征2中椭圆曲线的根数
DOI：
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发表时间：
2006
期刊：
影响因子：
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通讯作者：
V. Dokchitser
中科院分区：
文献类型：
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作者：
T. Dokchitser;V. Dokchitser
为了确定定义在数域上的椭圆曲线的全局根数，需要理解所有的局部根数。这些已被分类，除了在2以上的地方，在本文中，我们试图完成分类。在大于2的地方，我们用范数剩余符号来表示局部根数，当野惯性通过循环商作用时，用显式一维特征根数来表示局部根数，当野惯性通过四元数商作用时，用显式一维特征根数来表示局部根数。
To determine the global root number of an elliptic curve defined over a number field, one needs to understand all the local root numbers. These have been classified except at places above 2, and in this paper we attempt to complete the classification. At places above 2, we express the local root numbers in terms of norm residue symbols in the case when wild inertia acts through a cyclic quotient, and in terms of root numbers of explicit 1‐dimensional characters in the case when wild inertia acts through a quaternionic quotient.