All Questions

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 ...

Let $D=\left(\frac{a,b}{\mathbb{Q}}\right)$ be a quaternion algebra over $\mathbb{Q}$. Suppose $D$ is ramified at a finite set $S$ of places and $\infty\in S$. It is known that the $S$-units (the unit ...

Does the following statement hold: Statement: For any $\epsilon > 0$, there exist a number field $k$ of degree $d_{\epsilon}$ over $\mathbb{Q}$ and an arithmetic hyperbolic surface  $\Gamma$ ...