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

Nekovář, Jan

Annales scientifiques de l'École Normale Supérieure, Série 4, Tome 41 (2008) no. 6, pp. 1003-1022.

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.

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.

Classification : 11G40, 11F41, 11G05
Keywords: Selmer groups, Hilbert modular forms
Mot clés : groupes de Selmer, formes modulaires de Hilbert

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