Toward equivariant Iwasawa theory, IV

Abstract

Let l be an odd prime number and K _$infin$/k a Galois extension of totally real number fields, with k/Q and K _$infin;/k _$infin; finite, where k _$infin$ is the cyclotomic Z _l -extension of k. In [RW2] a "main conjecture" of equivariant Iwasawa theory is formulated which for pro-l groups G _$infin$ is reduced in [RW3] to a property of the Iwasawa L-function of K _$infin$/k. In this paper we extend this reduction for arbitrary G _$infin$ to l-elementary groups G _$infin$=$lang$s$rang$ x U, with $lang$s$rang$ a finite cyclic group of order prime to l and U a pro-l group. We also give first nonabelian examples of groups G _$infin$ for which the conjecture holds.