论文标题
SU（D，1）的算术亚组扩展的剩余有限性（d，1）
Residual finiteness of extensions of arithmetic subgroups of SU(d,1) with cusps
论文作者
论文摘要
令$γ$为$ su（d，1）$的算术子组，然后让$x_γ$为相关的本地对称空间。我们证明，如果第一个内部共同体学组$ h^1 _！（x_γ，\ mathbb {c}）$是非零的，则在$ su（d，1）$的每个连接的封面中，$γ$的前图是$γ$的。我们还举例说明了这样一个$ h^1 _！（x_γ，\ mathbb {c}）$的$γ$的示例。
Let $Γ$ be an arithmetic subgroup of $SU(d,1)$ with cusps, and let $X_Γ$ be the associated locally symmetric space. We prove that if the first inner cohomology group $H^1_!(X_Γ,\mathbb{C})$ is non-zero then the pre-image of $Γ$ in each connected cover of $SU(d,1)$ is residually finite. We also give an example of a such a group $Γ$ for which $H^1_!(X_Γ,\mathbb{C})$ is non-zero.
