论文标题
$ \ ell $ torsion in Class组的点数：小学Abelian Extensions
Pointwise Bound for $\ell$-torsion in Class Groups: Elementary Abelian Extensions
论文作者
论文摘要
基本的Abelian组是$ a =（\ Mathbb {z}/p \ Mathbb {z}）^r $的有限组。对于每个整数$ \ ell> 1 $和$ r> 1 $，我们证明在每$ a $ a $ extension的$ \ ell $ torsion上都有一个非平凡的上限。我们的结果是侧重和无条件的。当$ r $足够大时，我们获得的点式界限也将破坏Ellenberg-Venkatesh在GRH下显示的先前最著名的界限。
Elementary abelian groups are finite groups in the form of $A=(\mathbb{Z}/p\mathbb{Z})^r$ for a prime number $p$. For every integer $\ell>1$ and $r>1$, we prove a non-trivial upper bound on the $\ell$-torsion in class groups of every $A$-extension. Our results are pointwise and unconditional. When $r$ is large enough, the pointwise bound we obtain also breaks the previously best known bound shown by Ellenberg-Venkatesh under GRH.
