An Equivariant Main Conjecture in Iwasawa Theory and the Coates-Sinnott Conjecture

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 \cite{Wi}. This equivariant version coincides with the version, which Ritter and Weiss formulated and proved for odd $p$ under the assumption $\mu=0$ in \cite{RW2}. Our proof combines the approach of Ritter and Weiss with ideas and techniques used by Greither and Popescu in \cite{GP2} in a recent proof of an equivalent formulation of the above EMC under the same assumptions ($p$ odd and $\mu=0$) as in \cite{RW2}. As an application of the EMC we prove the Coates-Sinnott Conjecture, again assuming $\mu=0$ and the 2-adic Main Conjecture.

2010 Mathematics Subject Classification: 11R23, 11R42, 14F42, 11R70, 11R33, 11R34

Keywords and Phrases: Iwasawa theory, global and p-adic L-functions, motivic cohomology, algebraic K-theory, Fitting ideals

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