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On Equivariant Characteristic Ideals of Real Classes

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Iwasawa Theory 2012

Part of the book series: Contributions in Mathematical and Computational Sciences ((CMCS,volume 7))

Abstract

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.

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Acknowledgements

It is a pleasure for the author to thank Dr. Malte Witte for many useful discussions on his “limit theorem”, as well as the referee for his careful reading of the manuscript.

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Authors and Affiliations

  1. UFRST, F-25030, Besancon, France

    Thong Nguyen Quang Do

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  1. Thong Nguyen Quang Do
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Correspondence to Thong Nguyen Quang Do .

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Editors and Affiliations

  1. Dept. of Mathematical Sciences, Durham University, Durham, United Kingdom

    Thanasis Bouganis

  2. Institute of Mathematics, University of Heidelberg, Heidelberg, Germany

    Otmar Venjakob

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Do, T.N.Q. (2014). On Equivariant Characteristic Ideals of Real Classes. In: Bouganis, T., Venjakob, O. (eds) Iwasawa Theory 2012. Contributions in Mathematical and Computational Sciences, vol 7. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-55245-8_13

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