论文标题
结的规范组成部分的算术$ 7_4 $
Arithmetic of the canonical component of the Knot $7_4$
论文作者
论文摘要
我们证明了dehn手术点的两个算术特性在$ \ mathrm {sl} _2（\ mathbf {c}）$的典型组件上 - 结$ 7_4 $的字符品种。首先是Dehn手术点的残留特性形成了无限的集合，为Chinburg，Reid和Stover的猜想提供了证据。第二个是Dehn手术点在椭圆形曲线的Mordell-Weil组中具有无限的顺序，该椭圆形曲线通过将规范成分的简单偶然性转化为Weierstrass形式而获得。
We prove two arithmetic properties of Dehn surgery points on the canonical component of the $\mathrm{SL}_2(\mathbf{C})$-character variety of the knot $7_4$. The first is that the residue characteristics of the ramified places of the Dehn surgery points form an infinite set, providing evidence for a conjecture of Chinburg, Reid, and Stover. The second is that the Dehn surgery points have infinite order in the Mordell-Weil group of the elliptic curve obtained by a simple birational transformation of the canonical component into Weierstrass form.
