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I guess the folllowing is a short explicit proof of Tits' result for this very special case, assuming CSP for $\rm{SL}_n(\bf{Z})$ (so this should be seen as a lenghty comment on the above answer). Th …

I assume you mean for $K$ to be an imaginary quadratic field (see Misha's comment). There have been computations of the homology for a substantial array of small values of the discriminant of $K$, by …

In this answer i will follow Yves' comment and add references. If $U = \mathbf{U}(R)$ with $\mathbf U$ an algebraic unipotent $\mathbb Q$-group then the two following facts hold : If $\Lambda \le U …

This is well-known, and you don't need semisimplicity for this to hold. You can prove it by considering congruence subgroups of $H(\mathcal O_k)$ as follows. Let $\mathfrak n$ be an ideal of $\mathcal …

Let $\mathbb H^2$ be the hyperbolic plane, on which $\Gamma$ acts properly discontinuously and cocompactly. Thus the quotient space $O = \Gamma \backslash \mathbb H^2$ is a closed hyperbolic surface w …