The Equivariant Tamagawa Number Conjecture for modular motives with coefficients in Hecke algebras

par Prof. Olivier FOUQUET (Université Paris-Sud)

mercredi 17 mai 2017, 10:30 → 11:30 Europe/Paris

Centre de conférences Marilyn et James Simons (IHES)

The Equivariant Tamagawa Number Conjecture (ETNC) of Kato is an awe-inspiring web of conjectures predicting the special values of L-functions of motives as well as their behaviors under the action of algebras acting on motives. In this talk, I will explain the statement of the ETNC with coefficients in Hecke algebras for motives attached to modular forms, show some consequences in Iwasawa theory and outline a proof (under mild hypotheses on the residual representation) using a combination of the methods of Euler and Taylor-Wiles systems.