All Questions

Suppose $M = K\backslash G/\Gamma$ is a quotient of a symmetric space by a lattice. I don't know all of the proper adjectives to apply here (e.g. what should be said about $G$ and so on), but I wouldn'...

$\DeclareMathOperator\GL{GL}$Let $G \subset M_{n\times n~}(\mathbb Z)$ be a finitely generated subgroup of $\GL(n,\mathbb Q)$ (i.e. $g\in G$ is an invertible matrix with entries in $\mathbb Z$). Then $...

Let $O$ be the ring of $S$-integers in a real quadratic number field. Let $G$ be an $S$-arithmetic subgroup of $SL_2(O)$ whose intersection with $SL_2(\mathbb Z)$ is not of finite index in $SL_2(\...

That is, is it true that there does not exist a lattice in $G = {\rm SO}(n,1)$ which contains the group of integer points of $G$ as a proper subgroup (obviously then of finite index)? if such a ...