2004/04/16 by J. Coates, T. Fukaya, K. Kato +2 · 1 citation
Mathematics · #math.NT
paper · pdf · doi:10.1007/s10240-004-0029-3
published as Publ. Math. I.H.E.S. 101, 163-208 (2005) · 39 pages
arxiv created 2004/04/16 · arxiv updated 2010/06/29
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.