“p-adic” presentation of surfaces
4
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On several occasions I heard about the following result: For "certain" lattices $Lambda$ in $SL_2(mathbb{R})$ , and almost any prime $p$ there exists a lattice $Gamma$ in $SL_2(mathbb{R})times SL_2(mathbb{Q}_p)$ and a compact subgroup $K$ of $SL_2(mathbb{R})times SL_2(mathbb{Q}_p)$ such that there is an isomorphism between $$ Lambda backslash SL_2(mathbb{R}) $$ and $$ Gamma backslash SL_2(mathbb{R})times SL_2(mathbb{Q}_p)/K. $$ I know how to prove this for $Lambda = SL_2(mathbb{Z})$ . Then $Gamma = SL_2(mathbb{Z}[1/p])$ (diagonally in $SL_2(mathbb{R})times SL_2(mathbb{Q}_p)$ ) and $K={1}times SL_2(mathbb{Z}_p)$ and the isomorphism is a quite easy map. I would like to find a reference for more general $Lambda$ , preferably with an explicit statement of the isomorphism and...