Geodesic
Integrality of a ratio of Petersson norms and level-lowering congruences
Kartik Prasanna1
1 Department of Mathematics, University of California, Los Angeles, CA 90095, United States
Annals of mathematics, Tome 163 (2006) no. 3, pp. 901-967.

Voir la notice de l'article provenant de la source Annals of Mathematics website

We prove integrality of the ratio $\langle f,f\rangle/\langle g,g\rangle$ (outside an explicit finite set of primes), where $g$ is an arithmetically normalized holomorphic newform on a Shimura curve, $f$ is a normalized Hecke eigenform on ${\rm {\rm GL}}(2)$ with the same Hecke eigenvalues as $g$ and $\langle,\rangle$ denotes the Petersson inner product. The primes dividing this ratio are shown to be closely related to certain level-lowering congruences satisfied by $f$ and to the central values of a family of Rankin-Selberg $L$-functions. Finally we give two applications, the first to proving the integrality of a certain triple product $L$-value and the second to the computation of the Faltings height of Jacobians of Shimura curves.
DOI : 10.4007/annals.2006.163.901

Kartik Prasanna 1

1 Department of Mathematics, University of California, Los Angeles, CA 90095, United States 
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Kartik Prasanna. Integrality of a ratio of Petersson norms and level-lowering congruences. Annals of mathematics, Tome 163 (2006) no. 3, pp. 901-967. doi : 10.4007/annals.2006.163.901. http://geodesic.mathdoc.fr/articles/10.4007/annals.2006.163.901/

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