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 
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/
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Voir la notice de l'article provenant de la source Math-Net.Ru

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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[10] I. V. Cherednik, “Uniformizatsiya diskretnymi podgruppami $PGL_2(k_w)\times PSL_2(k_v)$”, Funkts. analiz, 9:2 (1975), 95–96 | MR | Zbl

[11] I. V. Cherednik, “Algebraicheskie krivye, uniformiziruemye diskretnymi arifmeticheskimi podgruppami $PGL_2(k_w)$”, Uspekhi matem. nauk, XXX:3 (183) (1975), 183–184

[12] I. V. Cherednik, “Uniformizatsiya algebraicheskikh krivykh diskretnymi arifmeticheskimi podgruppami $PGL_2(k_w)$ s kompaktnymi faktor-prostranstvami”, Matem. sb., 100(142):1(5) (1976), 59–88 | MR | Zbl