On the equivariant main conjecture of Iwasawa theory

Abstract

Recently, D. Burns and C. Greither (Invent. Math., 2003) deduced an equivariant version of the main conjecture for abelian number fields. This was the key to their proof of the equivariant Tamagawa number conjecture. A. Huber and G. Kings (Duke Math. J., 2003) also use a variant of the Iwasawa main conjecture to prove the Tamagawa number conjecture for Dirichlet motives. We use the result of the second pair of authors and the Theorem of Ferrero-Washington to reprove the equivariant main conjecture in a slightly more general form. The main idea of the proof is essentially the same as in the paper of D. Burns and C. Greither, but we can replace complicated considerations of Iwasawa $mu$-invariants by a considerably simpler argument.Comment: 24 pages, minor changes, final version, to appear in Acta Arithmetic