  We discuss three different formulations of the equivariant Iwasawa main
conjecture attached to an extension K/k of totally real fields with Galois
group G, where k is a number field and G is a p-adic Lie group of dimension 1
for an odd prime p. All these formulations are equivalent and hold if Iwasawa's
\mu-invariant vanishes. Under mild hypotheses, we use this to prove non-abelian
generalizations of Brumer's conjecture, the Brumer-Stark conjecture and a
strong version of the Coates-Sinnott conjecture provided that \mu = 0.
