[Sur la série caractéristique des groupes de Selmer signés]
Nous relions la cardinalité de la composante -primaire du groupe Selmer de Bloch–Kato sur associé à une forme modulaire en un nombre premier non-ordinaire au terme constant de la série caractéristique du groupe de Selmer signés le long de la -extension cyclotomique de . Ceci généralise un résultat de Vigni et Longo dans le cas ordinaire. Dans le cas des courbes elliptiques, de tels résultats découlent des travaux de Greenberg, Kim, du deuxième auteur, et d’Ahmed–Lim, qui englobent le cas ordinaire et la plupart des cas supersinguliers.
We relate the cardinality of the -primary part of the Bloch–Kato Selmer group over attached to a modular form at a non-ordinary prime to the constant term of the characteristic power series of the signed Selmer groups over the cyclotomic -extension of . This generalizes a result of Vigni and Longo in the ordinary case. In the case of elliptic curves, such results follow from earlier works by Greenberg, Kim, the second author, and Ahmed–Lim, covering both the ordinary and most of the supersingular case.
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Keywords: Euler characteristic, modular forms, signed Selmer groups, algebraic $p$-adic $L$-function
Mots-clés : caractéristique d’Euler, formes modulaires, groupes de Selmer signés, fonctions $L$ $p$-adiques algébriques
Ray, Jishnu 1 ; Sprung, Florian ITO 2
@unpublished{AIF_0__0_0_A148_0,
author = {Ray, Jishnu and Sprung, Florian ITO},
title = {On characteristic power series of dual signed {Selmer} groups},
journal = {Annales de l'Institut Fourier},
publisher = {Association des Annales de l{\textquoteright}institut Fourier},
year = {2025},
doi = {10.5802/aif.3702},
language = {en},
note = {Online first},
}
Ray, Jishnu; Sprung, Florian ITO. On characteristic power series of dual signed Selmer groups. Annales de l'Institut Fourier, Online first, 17 p.
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