The GL_2 main conjecture for elliptic curves without complex multiplication

Abstract: The main conjectures of Iwasawa theory provide the only general method
known at present for studying the mysterious relationship between
purely arithmetic problems and the special values of complex
$L$-functions, typified by the conjecture of Birch and Swinnerton-Dyer and
its generalizations. Our goal in the present paper is to develop
algebraic techniques which enable us to formulate a precise version of
such a main conjecture for motives over a large class of $p$-adic Lie
extensions of number fields. The methods which we develop in general were
inspired by the Heidelberg Habilitation thesis of Venjakob. |