论文标题
$ \ ell $ -torsion范围用于类数字字段的$ \ ell $ -group作为Galois组
$\ell$-torsion bounds for the class group of number fields with an $\ell$-group as Galois group
论文作者
论文摘要
我们描述了$ \ ell $ torsion的猜想之间的关系，Malle的猜想给了扩展次数的上限以及判别多重性猜想。我们证明后两个猜想在某种意义上是等效的。总体而言，这三个猜想对于可解决的组类别是等效的。然后，我们证明了$ \ ell $ -groups的$ \ ell $ -torsion猜想，而对尼尔普特组的其他两个猜想。
We describe the relations among the $\ell$-torsion conjecture, a conjecture of Malle giving an upper bound for the number of extensions, and the discriminant multiplicity conjecture. We prove that the latter two conjectures are equivalent in some sense. Altogether, the three conjectures are equivalent for the class of solvable groups. We then prove the $\ell$-torsion conjecture for $\ell$-groups and the other two conjectures for nilpotent groups.
