Geodesic
Uniformization of algebraic curves by discrete arithmetic subgroups of $PGL_2(k_w)$ with compact quotients
Sbornik. Mathematics, Tome 29 (1976) no. 1, pp. 55-78 
I. V. Cherednik. Uniformization of algebraic curves by discrete arithmetic subgroups of $PGL_2(k_w)$ with compact quotients. Sbornik. Mathematics, Tome 29 (1976) no. 1, pp. 55-78. http://geodesic.mathdoc.fr/item/SM_1976_29_1_a4/
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Voir la notice de l'article provenant de la source Math-Net.Ru

We consider curves having either a uniformization by the upper half-plane or a Mumford uniformization by discrete arithmetic subgroups of $PGL_2(k_w)$ corresponding to quaternion algebras with center $k$, with $k$ a global field of (possibly nonzero) characteristic $p$, $k$ being totally real if $p = 0$; $k_w$ is the completion of $k$ with respect to a valuation $w$ which is real or non-Archimedean. The principal result is a theorem that in characteristic $p = 0$ the curves corresponding to algebras related in a certain sense coincide. Bibliography: 10 titles.

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

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

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

[7] I. V. Cherednik, “Bashni algebraicheskikh krivykh, uniformiziruemye diskretnymi podgruppami $PGL_2(k_w)\times E$”, Matem. sb., 99 (141) (1976), 211–247 | Zbl

[8] G. Shimura, “Construction of class fields and zeta functions of algebraic curves”, Ann. Math., 85 (1967), 58–159 | DOI | MR | Zbl

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

[10] M. Eichler, “Zur Zahlentheorie der Quaternionenalgebren”, J. Reine Angew. Math., 195 (1956), 127–151 | MR