Geodesic
Towers of algebraic curves uniformized by discrete subgroups of $PGL_2(k_w)\times E$
Sbornik. Mathematics, Tome 28 (1976) no. 2, pp. 187-215

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Ihara, in his article “On congruence monodromy problems” showed that for a non-Archimedean local field $k_v$ one can associate to the discrete subgroups of $PSL_2(\mathbf R)\times PSL_2(k_v)$ of a certain type towers of algebraic curves on which $PSL_2(k_v)$ acts as a group of automorphisms. In the present article Ihara's results are carried over by means of Mumford's non-Archimedean uniformization to an analogous class of discrete subgroups of $PGL_2(k_w)\times E$, with $k_w$ a non-Archimedean field (of arbitrary characteristic), and $E$ a topological group whose compact open subgroups form a fundamental system of neighborhoods of $1$. Bibliography: 12 titles. 
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     author = {I. V. Cherednik},
     title = {Towers of algebraic curves uniformized by discrete subgroups of $PGL_2(k_w)\times E$},
     journal = {Sbornik. Mathematics},
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     volume = {28},
     number = {2},
     year = {1976},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/SM_1976_28_2_a4/}
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I. V. Cherednik. Towers of algebraic curves uniformized by discrete subgroups of $PGL_2(k_w)\times E$. Sbornik. Mathematics, Tome 28 (1976) no. 2, pp. 187-215. http://geodesic.mathdoc.fr/item/SM_1976_28_2_a4/