Comptes Rendus
Algebraic Geometry/Group Theory
Jacobians of modular curves associated to normalizers of Cartan subgroups of level pn
Comptes Rendus. Mathématique, Volume 339 (2004) no. 3, pp. 187-192.

We derive a relation between induced representations of the group GL2(Z/pnZ) which implies a relation between the Jacobians of certain modular curves of level pn. A consequence of this relation is that the Jacobian of the modular curve associated to the normalizer of a non-split Cartan subgroup of GL2(Z/pnZ) does not have any non-zero rank 0 quotient defined over Q if the Birch and Swinnerton–Dyer conjecture holds for Abelian varieties.

Nous établissons une relation entre des représentations induites du groupe GL2(Z/pnZ), ce qui implique une relation entre les jacobiennes de certaines courbes modulaires de niveau pn. Une conséquence de cette relation est que la jacobienne de la courbe modulaire associée au normalisateur d'un sous-groupe Cartan non-déployé de GL2(Z/pnZ) n'a aucun quotient non-nul de rang 0 défini sur Q si l'on admet la conjecture de Birch et Swinnerton–Dyer pour les variétés abéliennes.

Received:
Accepted:
Published online:
DOI: 10.1016/j.crma.2004.04.027
Imin Chen 1

1 Department of Mathematics, Simon Fraser University, Burnaby V5A 1S6, B.C., Canada
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Imin Chen. Jacobians of modular curves associated to normalizers of Cartan subgroups of level $ {p}^{n}$. Comptes Rendus. Mathématique, Volume 339 (2004) no. 3, pp. 187-192. doi : 10.1016/j.crma.2004.04.027. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.1016/j.crma.2004.04.027/

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