| 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. |