| Résume | Over the last few years Flach and the author have togetherformulated and studied a natural refinement of the seminal TamagawaNumberConjecture (as originally formulated by Bloch and Kato and then extendedandreworked by Fontaine and Perrin-Riou) in the context of motives with(non-commutative) coefficients. We aim to describe the basic formalismofthis equivariant refinement, review some of the currently availableevidence(in particular, in the context of Tate motives) and briefly explainsomestriking connections to certain other well known and more explicitconjectures (for example, of Mazur-Tate, Bertolini-Darmon, Gross,Gross-Tate, Rubin, Brumer, Coates-Sinnott, Chinburg..) |
