The arithmetic-groups tag has no wiki summary.

**8**

votes

**0**answers

350 views

### A uniform bound for a “true” non-congruence subgroup

Before stating my question, let me recall the Congruence Subgroup Property/Problem: Given simply connected absolutely and almost simple algebraic group $G$ with fixed realization as a matrix group one ...

**7**

votes

**0**answers

241 views

### subgroups of higher rank lattices

This is related to the question $G=\langle a\rangle H$ for subgroup $H$ raised a few days ago. Suppose $\Gamma $ is a higher rank lattice (for example, $SL_3({\mathbb Z})$). As Misha says in his ...

**5**

votes

**0**answers

187 views

### Generating congruence subgroups of SL_n over totally imaginary number rings

Fix some $n \geq 3$. Let $k$ be an algebraic number field with ring of integers $\mathcal{O}$ and let $\alpha$ be an ideal of $\mathcal{O}$. Define $\text{SL}_n(\mathcal{O},\alpha)$ to be the ...

**5**

votes

**0**answers

221 views

### Generators for SL_2(R) for rings of integers R

Let $\mathcal{O}$ be the ring of integers in an algebraic number field. Is $\text{SL}_2(\mathcal{O})$ generated by elementary matrices? If it isn't, is there any other natural generating set for it?
...

**4**

votes

**0**answers

198 views

### links and interactions between different approaches to (super-)rigidity

By super-rigidity I mean some theorems concerning the arithmetic subgroups in semi-simple Lie groups. According to Margulis "Discrete subgroups of semi-simple Lie groups" (the book published by ...

**2**

votes

**0**answers

133 views

### Discussion of specific arithmetic triangle groups?

Arithmetic triangle groups were classified in Takeuchi, Arithmetic triangle groups, J. Math. Soc. Japan Volume 29, Number 1 (1977), 91-106. The (2,3,7) case was discussed in detail in a number of ...

**1**

vote

**0**answers

156 views

### Compactifications of group schemes

Let $G$ be a group scheme over a scheme $S$ which is the spectrum of a discrete valuation ring. Let $\eta$ (resp. $s$) be the generic (resp. closed) point. Assume that the generic fiber $G_{\eta}$ is ...