The Bloch-Kato conjecture for adjoint motives of modular forms

Fred Diamond, Matthias Flach, Li Guo

Research output: Contribution to journalArticlepeer-review

8 Scopus citations

Abstract

The Tamagawa number conjecture of Bloch and Kato describes the behavior at integers of the L-function associated to a motive over Q. Let f be a newform of weight k ≥ 2, level N with coefficients in a number field K. Let M be the motive associated to f and let A be the adjoint motive of M. Let λ be a finite prime of K. We verify the λ-part of the Bloch-Kato conjecture for L(A, 0) and L(A, 1) when λ ł Nk! and the mod λ representation associated to f is absolutely irreducible when restricted to the Galois group over Q (√ (-1)(ℓ-1)/2ℓ) where λ | ℓ.

Original languageEnglish (US)
Pages (from-to)437-442
Number of pages6
JournalMathematical Research Letters
Volume8
Issue number4
DOIs
StatePublished - 2001

ASJC Scopus subject areas

  • Mathematics(all)

Keywords

  • Adjoint motive
  • Bloch-Kato conjecture
  • Modular forms

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