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 language | English (US) |
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Pages (from-to) | 437-442 |
Number of pages | 6 |
Journal | Mathematical Research Letters |
Volume | 8 |
Issue number | 4 |
DOIs | |
State | Published - 2001 |
ASJC Scopus subject areas
- Mathematics(all)
Keywords
- Adjoint motive
- Bloch-Kato conjecture
- Modular forms