On equivariant characteristic ideals of real classes

TL;DR

This paper explicitly describes the equivariant characteristic ideal of certain Iwasawa cohomology groups over an Iwasawa algebra for abelian totally real fields, using Witte's formulation of an equivariant main conjecture, with implications for Greenberg's conjecture.

Contribution

It provides an explicit description of the equivariant characteristic ideal of Iwasawa cohomology groups for all odd integers m, advancing understanding of the equivariant main conjecture.

Findings

Explicit formula for the equivariant characteristic ideal over the Iwasawa algebra.

Application of Witte's formulation to abelian totally real fields.

Insights into Greenberg's conjecture on the λ-invariant.

Abstract

Let $p$ be an odd prime, $F/{\Bbb Q}$ an abelian totally real number field, $F_\infty/F$ its cyclotomic ${\Bbb Z}_p$-extension, $G_\infty = Gal (F_\infty / {\Bbb Q}),$ ${\Bbb A} = {\Bbb Z}_p [[G_\infty]].$ We give an explicit description of the equivariant characteristic ideal of $H^2_{Iw} (F_\infty, {\Bbb Z}_p(m))$ over ${\Bbb A}$ for all odd $m \in {\Bbb Z}$ 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 $\lambda$-invariant of $F_\infty/F.$