Jacobians of modular curves associated to normalizers of Cartan subgroups of level [formula omitted

Abstract

We derive a relation between induced representations of the group GL 2 ( Z / p n Z ) which implies a relation between the Jacobians of certain modular curves of level p n . A consequence of this relation is that the Jacobian of the modular curve associated to the normalizer of a non-split Cartan subgroup of GL 2 ( Z / p n Z ) does not have any non-zero rank 0 quotient defined over Q if the Birch and Swinnerton–Dyer conjecture holds for Abelian varieties. To cite this article: I. Chen, C. R. Acad. Sci. Paris, Ser. I 339 (2004).