论文标题
$ \ mathrm {sl} _ {2} $的第三个同源性数字字段：norm-euclidean二次假想案例
Third homology of $\mathrm{SL}_{2}$ over Number fields: The norm-Euclidean quadratic imaginary case
论文作者
论文摘要
在文章中，$ sl_ {2}（\ Mathbb {q}）$的第三个同源性确定了$ h_ {3} \ left的结构用$ k_ {3}^{\ mathrm {indrm {indrm {indrm {indbb {q}）\ cong \ mathbb {z}/24 $表达它。在本文中，我们进一步开发了精制的剪刀一致性组的属性，以将此结果扩展到假想的二次数字字段的情况下，其整数是相对于规范的欧几里得域。
In the article The third homology of $SL_{2}(\mathbb{Q})$, Hutchinson determined the structure of $H_{3}\left(\mathrm{SL}_{2}(\mathbb{Q}),\mathbb{Z}\left[\frac{1}{2}\right]\right)$ by expressing it in terms of $K_{3}^{\mathrm{ind}}(\mathbb{Q})\cong \mathbb{Z}/24$ and the scissor congruence group of the residue field $\mathbb{F}_{p}$ with $p$ a prime number. In this paper, we develop further the properties of the refined scissors congruence group in order to extend this result to the case of imaginary quadratic number fields whose ring of integers is a Euclidean domain with respect to the norm.
