Toward equivariant Iwasawa theory, IV

Jürgen Ritter and Alfred Weiss

Let l be an odd prime number and K_∞/k a Galois extension of totally real number fields, with k/Q and K_∞/k_∞ finite, where k_∞ 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_∞ is reduced in [RW3] to a property of the Iwasawa L-function of K_∞/k. In this paper we extend this reduction for arbitrary G_∞ to l-elementary groups G_∞=⟨s⟩×U, with ⟨s⟩ a finite cyclic group of order prime to l and U a pro-l group. We also give first nonabelian examples of groups G_∞ for which the conjecture holds.

Homology, Homotopy and Applications, Vol. 7 (2005), No. 3, pp.155-171.

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