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

Masataka Chida

Research output: Contribution to journalArticlepeer-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 languageEnglish
Pages (from-to)1231-1276
Number of pages46
JournalAnnales de l'Institut Fourier
Volume67
Issue number3
DOIs
Publication statusPublished - 2017

Keywords

  • Bloch-Kato conjecture
  • Modular forms
  • Selmer groups

ASJC Scopus subject areas

  • Algebra and Number Theory
  • Geometry and Topology

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