# Tagged Questions

**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

**1**answer

553 views

### Why are $S$-arithmetic groups interesting?

Let $K$ be a number field and $S$ a finite set of valuations of $K$, including $\infty$.
Define the $S$-numbers $K_S$ to be the direct product $\prod_{s \in S} K_s$ where $K_s$ denotes the completion ...

**7**

votes

**4**answers

968 views

### cohomology of moduli spaces

Does anyone know if there's any reference on the $\ell$-adic cohomology of some simple moduli spaces/Shimura varieties, like Siegel moduli varieties $A_{g,N}$ of genus $g$ and level $N,$ for small $g$ ...