Equivariant Tamagawa Number Conjectures
(Un exposé de David Burns au séminaire de théorie
des nombres de Chevaleret le 24 juin 2002)
Résumé :
Over the last few years Flach and the author have together
formulated and studied a natural refinement of the seminal Tamagawa
Number
Conjecture (as originally formulated by Bloch and Kato and then extended
and
reworked by Fontaine and Perrin-Riou) in the context of motives with
(non-commutative) coefficients. We aim to describe the basic formalism
of
this equivariant refinement, review some of the currently available
evidence
(in particular, in the context of Tate motives) and briefly explain
some
striking connections to certain other well known and more explicit
conjectures (for example, of Mazur-Tate, Bertolini-Darmon, Gross,
Gross-Tate, Rubin, Brumer, Coates-Sinnott, Chinburg..)