On equivariant characteristic ideals of real classes

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_{...

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Bibliographic Details
Published inarXiv.org
Main Author Thong Nguyen Quang Do
Format Paper
LanguageEnglish
Published Ithaca Cornell University Library, arXiv.org 28.05.2013
Subjects
Number theory
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Summary: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 \(F_\infty/F.\)
ISSN:2331-8422