An Equivariant Main Conjecture in Iwasawa theory without the assumption μ = 0

Abstract

The Equivariant Main Conjecture (EMC) in Iwasawa theory has been formulated and proved by Ritter–Weiss [14] and differently – but equivalently – by Greither–Popescu [4] for odd primes under the assumption μ=0. In [17] we extended the EMC of Ritter–Weiss to all prime numbers, and proved it assuming μ=0 and for p=2 the validity of the 2-adic Main Conjecture. In this paper we are going even further by dropping the assumption μ=0.