论文标题
Cassels-Tate配对的现场更改和对课程组的应用
Field change for the Cassels-Tate pairing and applications to class groups
论文作者
论文摘要
在先前的工作中，作者定义了一个有限的Galois模块的类别$ SMOD_F $，该模块装饰了每个全局字段$ f $。在本文中，给定全球字段的扩展名$ k/f $，我们将标量函数的限制从$ smod_k $到$ smod_f $，并表明它与纸牌配对相对良好。我们将这项工作应用于Cohen-Lenstra启发式方法的背景下研究全球领域的阶级群体。
In previous work, the authors defined a category $SMod_F$ of finite Galois modules decorated with local conditions for each global field $F$. In this paper, given an extension $K/F$ of global fields, we define a restriction of scalars functor from $SMod_K$ to $SMod_F$ and show that it behaves well with respect to the Cassels-Tate pairing. We apply this work to study the class groups of global fields in the context of the Cohen-Lenstra heuristics.
