Growth of Selmer groups of Hilbert modular forms over ring class fields
Annales scientifiques de l'École Normale Supérieure, Serie 4, Volume 41 (2008) no. 6, p. 1003-1022

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.

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.

DOI : https://doi.org/10.24033/asens.2087
Classification:  11G40,  11F41,  11G05
Keywords: Selmer groups, Hilbert modular forms
@article{ASENS_2008_4_41_6_1003_0,
     author = {Nekov\'a\v r, Jan},
     title = {Growth of Selmer groups of Hilbert modular forms over ring class fields},
     journal = {Annales scientifiques de l'\'Ecole Normale Sup\'erieure},
     publisher = {Soci\'et\'e math\'ematique de France},
     volume = {Ser. 4, 41},
     number = {6},
     year = {2008},
     pages = {1003-1022},
     doi = {10.24033/asens.2087},
     zbl = {1236.11047},
     mrnumber = {2504111},
     language = {en},
     url = {http://www.numdam.org/item/ASENS_2008_4_41_6_1003_0}
}
Nekovář, Jan. Growth of Selmer groups of Hilbert modular forms over ring class fields. Annales scientifiques de l'École Normale Supérieure, Serie 4, Volume 41 (2008) no. 6, pp. 1003-1022. doi : 10.24033/asens.2087. http://www.numdam.org/item/ASENS_2008_4_41_6_1003_0/

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