This article is cited in 2 papers

The rational points on the Jacobians of modular curves

V. G. Berkovich


Abstract: In this paper a theorem on the rank of the group of rational points of an Abelian variety with a sufficiently large ring of endomorphisms is proved. It is applied to construct nontrivial factors of the Jacobians of modular curves with finite groups of rational points and to prove finiteness theorems for modular curves.
Bibliography: 20 titles.

UDC: 513.015.7

MSC: Primary 10D20, 14K15; Secondary 14G25, 10D05, 14H40

Received: 02.02.1976

 English version: Mathematics of the USSR-Sbornik, 1976, 30:4, 478–500

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