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 Cet article a éte moissonné depuis la source Math-Net.Ru

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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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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/

[1] A. Veil, Osnovy teorii chisel, izd-vo «Mir», Moskva, 1972 | MR

[2] A. Grotendieck, Fondements de la géométrie algébrique, Secrétariat mathématique, Paris, 1962

[3] Ya. Ikhara, “O zadachakh kongruents-monodromii”, Matematika, 14:3 (1970), 40–98 | Zbl

[4] Ya. Ikhara, “O diskretnykh podgruppakh proektivnoi lineinoi gruppy vtorogo poryadka nad $p$-adicheskimi polyami”, Matematika, 12:3 (1968), 98–115

[5] M. Kneser, “Strong approximation”, Proc. Symposia in pure math., IX (1966), 187–196 | MR

[6] D. Mamford, “Analiticheskaya konstruktsiya krivykh s vyrozhdennoi reduktsiei nad polnymi lokalnymi koltsami”, Uspekhi matem. nauk, XXVII:6 (168) (1972), 181–221 | MR

[7] V. P. Platonov, “Problema silnoi approksimatsii i gipoteza Knezera-Titsa dlya algebraicheskikh grupp”, Izv. AN SSSR, seriya matem., 33 (1969), 1211–1220 | MR

[8] Zh. P. Serr, “Derevya, amalgamy i $SL_2$”, Matematika, 18:1 (1974), 3–51 | Zbl

[9] G. Shimura, Vvedenie v arifmeticheskuyu teoriyu avtomorfnykh funktsii, izd-vo «Mir», Moskva, 1973 | MR

[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