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Let p be an odd prime, \(F/\mathbb{Q}\) an abelian totally real number field, F ∞ ∕F its cyclotomic \(\mathbb{Z}_{p}\)-extension, \(G_{\infty } = \text{Gal}(F_{\infty }/\mathbb{Q}),\ \mathbb{A} = \mathbb{Z}_{p}[[G_{\infty }]].\) We give an explicit description of the equivariant characteristic ideal of \(H_{Iw}^{2}(F_{\infty }, \mathbb{Z}_{p}(m))\) over \(\mathbb{A}\) for all odd \(m \in \mathbb{Z}\) by applying M. Witte’s formulation of an equivariant main conjecture (or “limit theorem”) due to Burns and Greither. This could shed some light on Greenberg’s conjecture on the vanishing of the λ-invariant of F ∞ ∕F.

On Equivariant Characteristic Ideals of Real Classes