Selmer groups and central values of L-functions for modular forms

Masataka Chida

doi:10.5802/aif.3108

Selmer groups and central values of L-functions for modular forms

Masataka Chida

SCI - Mathematics

Research output: Contribution to journal › Article › peer-review

3 Citations (Scopus)

Abstract

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.

Original language	English
Pages (from-to)	1231-1276
Number of pages	46
Journal	Annales de l'Institut Fourier
Volume	67
Issue number	3
DOIs	https://doi.org/10.5802/aif.3108
Publication status	Published - 2017

Keywords

Bloch-Kato conjecture
Modular forms
Selmer groups

ASJC Scopus subject areas

Algebra and Number Theory
Geometry and Topology

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AB - 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.

KW - Bloch-Kato conjecture

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KW - Selmer groups

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Selmer groups and central values of L-functions for modular forms

Abstract

Keywords

ASJC Scopus subject areas

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