论文标题
在$ \ mathbb {z} _p $ - extension的未受到的iWasawa模块上，由CM椭圆曲线的划分生成
On the unramified Iwasawa module of a $\mathbb{Z}_p$-extension generated by division points of a CM elliptic curve
论文作者
论文摘要
我们考虑了一个未经夸大的iwasawa模块$ x（f_ \ infty）$的特定$ \ mathbb {z} _p $ - extension $ f_ \ f_ \ infty/f_0 $，由带有复杂乘法的椭圆曲线的分区点生成。这个$ \ mathbb {z} _p $ - extension的属性类似于环形元素$ \ mathbb {z} _p $ - 真正的亚伯利亚领域的extension，但是，已经知道$ x（f_ \ infty）$可以是无限的。也就是说，Greenberg的猜想的类似物对此$ \ Mathbb {z} _p $ - 延迟失败。在本文中，我们主要考虑格林伯格猜想的弱形式的类似物。
We consider the unramified Iwasawa module $X (F_\infty)$ of a certain $\mathbb{Z}_p$-extension $F_\infty/F_0$ generated by division points of an elliptic curve with complex multiplication. This $\mathbb{Z}_p$-extension has properties similar to those of the cyclotomic $\mathbb{Z}_p$-extension of a real abelian field, however, it is already known that $X (F_\infty)$ can be infinite. That is, an analog of Greenberg's conjecture for this $\mathbb{Z}_p$-extension fails. In this paper, we mainly consider analogs of weak forms of Greenberg's conjecture.
