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

Voir la notice de l'article

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. 
@article{SM_1976_29_1_a4,
     author = {I. V. Cherednik},
     title = {Uniformization of algebraic curves by discrete arithmetic subgroups of $PGL_2(k_w)$ with compact quotients},
     journal = {Sbornik. Mathematics},
     pages = {55--78},
     year = {1976},
     volume = {29},
     number = {1},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/SM_1976_29_1_a4/}
}
TY  - JOUR
AU  - I. V. Cherednik
TI  - Uniformization of algebraic curves by discrete arithmetic subgroups of $PGL_2(k_w)$ with compact quotients
JO  - Sbornik. Mathematics
PY  - 1976
SP  - 55
EP  - 78
VL  - 29
IS  - 1
UR  - http://geodesic.mathdoc.fr/item/SM_1976_29_1_a4/
LA  - en
ID  - SM_1976_29_1_a4
ER  - 
%0 Journal Article
%A I. V. Cherednik
%T Uniformization of algebraic curves by discrete arithmetic subgroups of $PGL_2(k_w)$ with compact quotients
%J Sbornik. Mathematics
%D 1976
%P 55-78
%V 29
%N 1
%U http://geodesic.mathdoc.fr/item/SM_1976_29_1_a4/
%G en
%F SM_1976_29_1_a4
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/

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

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

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

[4] D. Mamford, “Analiticheskaya konstruktsiya krivykh s vyrozhdennoi reduktsiei nad polnymi lokalnymi koltsami”, Uspekhi matem. nauk, XXVII:6(165) (1972), 181–221 | MR

[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