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Zbl 0599.14032
Gekeler, Ernst-Ulrich
Über Drinfeld'sche Modulkurven vom Hecke-Typ. (On Drinfel'd modular curves of Hecke type). (German)
[J] Compos. Math. 57, 219-236 (1986). ISSN 0010-437X; ISSN 1570-5846/e

The purpose of this paper is to investigate the Drinfeld modular curve $X\sb 0(n)$ by reduction mod(n), where (n) denotes a finite prime place of rational function field over a finite field. Among others, the author evaluates the order of the cusp divisor class of $X\sb 0(n)$ (in {\S} 4) using the idea of Ogg and the results of Raynaud [{\it A. P. Ogg}, Analytic number theory, Proc. Symp. Pure Math. 24, St. Louis Univ., Missouri 1982, 211-231 (1973; Zbl 0273.14008), {\it M. Raynaud}, Publ. Math., Inst. Hautes Étud. Sci. 38, 27-76 (1970; Zbl 0207.51602)].
[K.Katayama]

MSC 2000:: *14H45 Special curves and curves of low genus
11G20 Curves over finite and local fields
11G18 Arithmetic aspects of modular and Shimura varieties
11R58 Arithmetic theory of algebraic function fields
14G15 Finite ground fields

Keywords: finite ground field; Drinfeld modular curve; order of the cusp divisor class; Atkin-Lehner involution

Citations: Zbl 0273.14008; Zbl 0207.51602

Cited in: Zbl 1119.11031 Zbl 0930.11031 Zbl 1045.11510

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