论文标题
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Bloch Groups of Rings
论文作者
论文摘要
我们给出了（精制）一般通勤环（精致）bloch群的定义，这些戒指与标准定义一致，而当地环的残留场至少具有$ 4 $元素。在环上的适当条件下，任何字段或本地环满足，这些组与$ \ mathrm {sl} _2（a）$的第三个同源物以及与$ a $ a $的$ k_3 $ a $密切相关。我们分析了这些条件。我们计算$ \ mathbb {f} _2，\ mathbb {f} _3，\ mathbb {z} $和$ \ mathbb {z} [\ frac {1} {2}] $的Bloch组。
We give a definition of (refined) Bloch groups of general commutative rings which agrees with the standard definition in the case of local rings whose residue field has at least $4$ elements. Under appropriate conditions on a ring $A$, satisfied by any field or local ring, these groups are closely related to third homology of $\mathrm{SL}_2(A)$ and to indecomposable $K_3$ of $A$. We analyze these conditions. We calculate the Bloch groups of $\mathbb{F}_2,\mathbb{F}_3,\mathbb{Z}$ and $\mathbb{Z}[\frac{1}{2}]$.
