An equivariant main conjecture in Iwasawa theory and the Coates-Sinnott conjecture

Abstract

We formulate and prove an Equivariant Main Conjecture (EMC) for \it all prime numbers p under the assumptions \mu = 0 and the validity of the 2-adic Main Conjecture in Iwasawa theory citeWi. This equivariant version coincides with the version, which Ritter and Weiss formulated and proved for odd p under the assumption \mu=0 in citeRW2. Our proof combines the approach of Ritter and Weiss with ideas and techniques used by Greither and Popescu in citeGP2 in a recent proof of an equivalent formulation of the above EMC under the same assumptions ( p odd and \mu=0 ) as in citeRW2. As an application of the EMC we prove the Coates-Sinnott Conjecture, again assuming \mu=0 and the 2-adic Main Conjecture.