Growth of Selmer groups of Hilbert modular forms over ring class fields

[Croissance des groupes de Selmer de formes modulaires de Hilbert sur des corps de classes d'anneau]

Nekovář, Jan

Annales scientifiques de l'École Normale Supérieure, Tome 41 (2008), p. 1003-1022 / Harvested from Numdam

Résumé

On donne des bornes inférieures non triviales sur la croissance des rangs des groupes de Selmer de formes modulaires de Hilbert sur les corps de classes d'anneau et sur des extensions de Kummer, en démontrant d'abord un résultat de parité.

Abstract

We prove non-trivial lower bounds for the growth of ranks of Selmer groups of Hilbert modular forms over ring class fields and over certain Kummer extensions, by establishing first a suitable parity result.

Détail

Publié le : 2008-01-01

MR 2504111 | Zbl 1236.11047

DOI : https://doi.org/10.24033/asens.2087
Classification:  11G40,  11F41,  11G05
Mots clés: groupes de Selmer, formes modulaires de Hilbert

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