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2 votes
2 answers
294 views

Cohomology of $S$-arithmetic groups with trivial coefficients such as $H^n(\rm{PGL}_2(\mathbb{Z}[1/N]);\mathbb{Z})$

As $\rm{PSL}(2,\mathbb{Z})=(\mathbb{Z}/2\mathbb{Z})*(\mathbb{Z}/3\mathbb{Z})$, its cohomology groups $H^n(\rm{PSL}(2,\mathbb{Z});\mathbb{Z})$ are easy to get. Let $N$ be a product of distinct primes. ...
9 votes
1 answer
212 views

Lower bounds for the top rational cohomology of arithmetic groups

I would like to know what estimates exist for the dimension of $H^d({\rm GL}_2(\mathcal{O}_{K,S}),\mathbb{Q})$ where $\mathcal{O}_{K,S}$ is a ring of $S$-integers in a number field $K$ and $d$ is the ...
7 votes
1 answer
397 views

Cohomology of certain arithmetic groups

This is a question on literature about cohomology of arithmetic groups. Let $M$ denote a quaternion algebra over $\mathbb Q$ and assume it is non-split over $\mathbb R$. Fix a maximal order $\Lambda$ ...