  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 paper ends by formulating
and briefly discussing the main conjecture for an elliptic curve E over the
rationals Q over the field generated by the coordinates of its p-power division
points, where p is a prime greater than 3 of good ordinary reduction for E.
