The GL_2 main conjecture for elliptic curves without complex multiplication

Details The GL_2 main conjecture for elliptic curves without complex multiplication The GL_2 main conjecture for elliptic curves without complex multiplication

2004-04-16

arxiv.org/abs/math/0404297v1

Publ. Math. I.H.E.S. 101, 163-208 (2005)

Mathematics

Number Theory

39 pages

Scientific paper

10.1007/s10240-004-0029-3

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.

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