Characteristic elements in non-commutative Iwasawa theory
(Un exposé d'Otmar Venjakob au séminaire de
théorie des nombres de Chevaleret le 2 février 2004)
Résumé :
Thanks to Rubin and others, the one and two variable Iwasawa theory
of elliptic curves with complex multiplication (CM) is well
understood.
On the other hand, not much is known about the $GL_2$ theory of
elliptic
curves without CM. The aim of the talk is to introduce characteristic
elements, i.e. algebraic $p$-adic $L$-functions, in this situation;
they live in certain localizations of the Iwasawa algebra. Finally,
we discuss the Iwasawa Main Conjecture in the $GL_2$ setting.