Adjoint Motives of Modular Forms and the Tamagawa Number Conjecture

@inproceedings{Flach2001AdjointMO,
  title={Adjoint Motives of Modular Forms and the Tamagawa Number Conjecture},
  author={Matthias Flach},
  year={2001}
}
This paper concerns the Tamagawa number conjecture of Bloch and Kato [B-K] for adjoint motives of modular forms of weight k ≥ 2. The conjecture relates the value at 0 of the associated L-function to arithmetic invariants of the motive. We prove that it holds up to powers of certain “bad primes.” The strategy for achieving this is essentially due to Wiles [Wi], as completed with Taylor in [T-W]. The Taylor-Wiles construction yields a formula relating the size of a certain module measuring… CONTINUE READING