Chevalley–Weil theorem and subgroups of class groups
Chevalley–Weil theorem and subgroups of class groups
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Chevalley–Weil 定理和类群的子群
DOI：
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发表时间：
2016
影响因子：
1
通讯作者：
J. Gillibert
中科院分区：
文献类型：
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作者：
Y. Bilu;J. Gillibert
我们证明，在一些温和的假设下，在数域上定义的曲线的“etale cover”具有无限多的特化，成为数域的无处不在的无分支扩展。这构成了切瓦利-韦尔定理的“绝对”版本。利用这个结果，我们能够推广 Mestre、Levin 和第二作者构建和计算大类群数字域的技术。
We prove, under some mild hypothesis, that an ´etale cover of curves defined over a number field has infinitely many specializations into an everywhere unramified extension of number fields. This constitutes an “absolute” version of the Chevalley–Weil theorem. Using this result, we are able to generalise the techniques of Mestre, Levin and the second author for constructing and counting number fields with large class group.