A generalization of level-raising congruences for algebraic modular forms

[Une généralisation des congruences d’augmentation du niveau pour des formes modulaires algébriques]

Mazanti Sorensen, Claus

Annales de l'Institut Fourier, Tome 56 (2006), p. 1735-1766 / Harvested from Numdam

Résumé

Dans cet article, on étend des résultats d’augmentation du niveau de Ribet et Taylor, au cas de formes modulaires algébriques pour une algèbre à division sur un corps totalement réel $F$. On travaille avec des représentations automorphes d’un groupe réductif $G$ sur $F$, compact à l’infini. Dans le cas particulier où $G$ est une forme intérieure de ${\rm GSp}(4)$ sur $\mathbb{Q}$, on utilise ces résultats pour construire des congruences entre des formes de Saito-Kurokawa et des formes avec des composantes locales génériques.

Abstract

In this paper, we extend the results of Ribet and Taylor on level-raising for algebraic modular forms on the multiplicative group of a definite quaternion algebra over a totally real field $F$. We do this for automorphic representations of an arbitrary reductive group $G$ over $F$, which is compact at infinity. In the special case where $G$ is an inner form of ${\rm GSp}(4)$ over $\mathbb{Q}$, we use this to produce congruences between Saito-Kurokawa forms and forms with a generic local component.

Détail

Publié le : 2006-01-01

MR 2282674 | Zbl pre05145727 | 1 citation dans Numdam

DOI : https://doi.org/10.5802/aif.2226
Classification:  11F33,  11F70
Mots clés: augmentation du niveau, formes modulaires algébriques

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