论文标题
阿德氏级超级和有限的孤立晶格
Adelic superrigidity and profinitely solitary lattices
论文作者
论文摘要
根据算术和超级汇率，较高等级的晶格组中的晶格类别是由一个唯一的代数组定义的，而不是$ \ mathbb {r} $或$ \ mathbb {c} $的唯一数字子字段。我们证明了超级汇率的Adelic版本，这意味着当且仅当代数组是同构同构的时，两个这样的可辨式类别定义了相同的涂鸦性可高度率类别。我们讨论了对僵化问题的值得注意的后果。
By arithmeticity and superrigidity, a commensurability class of lattices in a higher rank Lie group is defined by a unique algebraic group over a unique number subfield of $\mathbb{R}$ or $\mathbb{C}$. We prove an adelic version of superrigidity which implies that two such commensurability classes define the same profinite commensurability class if and only if the algebraic groups are adelically isomorphic. We discuss noteworthy consequences on profinite rigidity questions.
