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1 vote
0 answers
95 views

Small pants in arithmetic hyperbolic surfaces of high degree

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  $\Gamma$ ...
5 votes
4 answers
700 views

Examples of discrete subgroups of $PSL_2(\mathbf{R})$ with finite covolume and which are not co-compact

Is there a natural example of a discrete subgroup $\Gamma\leq PSL_2(\mathbf{R})$ such that (1) $\Gamma$ has finite covolume (2) $\mathfrak{h}/\Gamma$ is not compact ($\mathfrak{h}$ being the upper ...