论文标题
$ \ ell^{\ infty} $ - selmer组的分布$ \ ell $ twist家庭ii ii
The distribution of $\ell^{\infty}$-Selmer groups in degree $\ell$ twist families II
论文作者
论文摘要
我们继续调查$ \ ell^{\ infty} $ - selmer组的分布，$ \ ell $ $ \ ell $ twist twist twist of galois模块的家族在上一篇论文中开始的数字字段。在该部分的高级Selmer组上建立工作，我们找到了可以计算给定程度$ \ ell $ twist家族的$ \ ell^{\ infty} $组的分布的条件。在此过程中，我们表明，任何给定的Abelian品种在数字字段中的平均级别的平均等级是有限的。
We continue the investigation of the distribution of $\ell^{\infty}$-Selmer groups in degree $\ell$ twist families of Galois modules over number fields begun in the previous paper. Building off the work on higher Selmer groups in that part, we find conditions under which we can compute the distribution of the $\ell^{\infty}$-Selmer groups for a given degree $\ell$ twist family. Along the way, we show that the average rank in the quadratic twist family of any given abelian variety over a number field is bounded.
