论文标题
在更高排名的谎言组中绝对有限地孤立的格子
On absolutely profinitely solitary lattices in higher rank Lie groups
论文作者
论文摘要
我们确定了某些简单谎言组中的晶格在绝对意义上是准确孤立的条件，以便在有限生成的残留有限的基团中，涂鸦完成的可相当性类别决定了该组的可低音性类别。虽然CoCompact晶格通常不是绝对单独的，但我们表明$ \ operatorname {sp}（n，n，\ m athbb {r}）$，$ g_ {2（2）} $，$ e_8（$ e_8（\ athbb {c}）$，$ f_4（c} $ mathbb}） $ g_2（\ mathbb {c}）$是绝对孤独的，如果对Grothendieck刚性的众所周知的猜想是正确的。
We establish conditions under which lattices in certain simple Lie groups are profinitely solitary in the absolute sense, so that the commensurability class of the profinite completion determines the commensurability class of the group among finitely generated residually finite groups. While cocompact lattices are typically not absolutely solitary, we show that noncocompact lattices in $\operatorname{Sp}(n,\mathbb{R})$, $G_{2(2)}$, $E_8(\mathbb{C})$, $F_4(\mathbb{C})$, and $G_2(\mathbb{C})$ are absolutely solitary if a well-known conjecture on Grothendieck rigidity is true.
