Relations between jacobians of modular curves of level $p^2$

Chen, Imin; De Smit, Bart; Grabitz, Martin

doi:10.5802/jtnb.435

Relations between jacobians of modular curves of level

p^{2}

Chen, Imin ¹ ; De Smit, Bart ² ; Grabitz, Martin ³

¹ Department of Mathematics Simon Fraser University Burnaby, B.C., Canada, V5A 1S6
² Mathematisch Instituut Universiteit Leiden Postbus 9512 2300 RA Leiden, Netherlands
³ Mathematisches Institut der Humboldt Universitaet Rudower Chaussee 25 (Ecke Magnusstrasse) 12489 Berlin House 1, Germany

Journal de théorie des nombres de Bordeaux, Tome 16 (2004) no. 1, pp. 95-106.

Résumé
Abstract

Nous établissons une relation entre les représentations induites sur le groupe ${GL}_{2} (ℤ / p^{2} ℤ)$ qui implique une relation entre les jacobiennes des certaines courbes modulaires de niveaux $p^{2}$ . La motivation de la construction de cette relation est la détermination de l’applicabilité de la méthode de Mazur à la courbe modulaire associée au normalisateur d’un subgroupe Cartan non-déployé de ${GL}_{2} (ℤ / p^{2} ℤ)$ .

We derive a relation between induced representations on the group ${GL}_{2} (ℤ / p^{2} ℤ)$ which implies a relation between the jacobians of certain modular curves of level $p^{2}$ . The motivation for the construction of this relation is the determination of the applicability of Mazur’s method to the modular curve associated to the normalizer of a non-split Cartan subgroup of ${GL}_{2} (ℤ / p^{2} ℤ)$ .

MR Zbl

DOI : 10.5802/jtnb.435

Affiliations des auteurs :

Chen, Imin ¹ ; De Smit, Bart ² ; Grabitz, Martin ³

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     title = {Relations between jacobians of modular curves of level $p^2$},
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Chen, Imin; De Smit, Bart; Grabitz, Martin. Relations between jacobians of modular curves of level $p^2$. Journal de théorie des nombres de Bordeaux, Tome 16 (2004) no. 1, pp. 95-106. doi : 10.5802/jtnb.435. https://www.numdam.org/articles/10.5802/jtnb.435/

Bibliographie
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