Résume | 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. |