no. 3
Selmer groups and central values of L-functions for modular forms
[Groupes de Selmer et valeurs centrales de fonctions L de formes modulaires]
Chida, Masataka1
1 Mathematical Institute Tohoku University 6-3, Aramaki Aza-Aoba, Aoba-ku Sendai 980-8578 (Japan)
Annales de l'Institut Fourier, Tome 67 (2017) no. 3, pp. 1231-1276.

Dans cet article, nous construisons un système d’Euler en utilisant les cycles CM sur les variétés de Kuga–Sato au-dessus de courbes de Shimura, et montrons une relation avec les valeurs centrales de fonctions L de Rankin–Selberg associées aux formes modulaires de poids 2 et aux caractères de classes d’un corps quadratique imaginaire. Comme application, nous prouvons que la non-annulation des valeurs centrales de fonctions L de Rankin–Selberg implique la finitude des groupes de Selmer associés à la représentation galoisienne de la forme modulaire sous certaines hypothèses.

In this article, we construct an Euler system using CM cycles on Kuga–Sato varieties over Shimura curves and show a relation with the central values of Rankin–Selberg L-functions for elliptic modular forms and ring class characters of an imaginary quadratic field. As an application, we prove that the non-vanishing of the central values of Rankin–Selberg L-functions implies the finiteness of Selmer groups associated to the corresponding Galois representation of modular forms under some assumptions.

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Révisé le :
Accepté le :
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DOI : 10.5802/aif.3108
Classification : 11F67, 11R23
Keywords: Modular forms, Selmer groups, Bloch–Kato conjecture
Mot clés : Formes modulaires, groupes de Selmer, conjecture de Bloch–Kato

Chida, Masataka 1

1 Mathematical Institute Tohoku University 6-3, Aramaki Aza-Aoba, Aoba-ku Sendai 980-8578 (Japan)
Licence : CC-BY-ND 4.0
Droits d'auteur : Les auteurs conservent leurs droits 
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Chida, Masataka. Selmer groups and central values of $L$-functions for modular forms. Annales de l'Institut Fourier, Tome 67 (2017) no. 3, pp. 1231-1276. doi : 10.5802/aif.3108. https://aif.centre-mersenne.org/articles/10.5802/aif.3108/

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