The Iwasawa main conjecture fields has been an important tool to study the
arithmetic of special values of L-functions of Hecke characters of imaginary
quadratic fields. To obtain the finest possible invariants it is important to
know the main conjecture for all prime numbers p and also to have an
equivariant version at disposal.
In this paper we first prove the main conjecture for imaginary quadratic
fields for all prime numbers p, improving earlier results by Rubin. From this
we deduce the equivariant main conjecture in the case that a certain
μ-invariant vanishes. For prime numbers p∤6 which split in K, this
is a theorem by a result of Gillard.Comment: 38 pages, completely revised version, inaccuracies and typos fixe