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Cyclotomic units and class groups in p-extensions of real abelian fields

Published online by Cambridge University Press:  16 June 2009

FILIPPO ALBERTO EDOARDO NUCCIO
FILIPPO ALBERTO EDOARDO NUCCIO*
Affiliation:
Università “La Sapienza”, P.le Aldo Moro, 5-00186, Rome, Italy. e-mail: [email protected]
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Abstract

For a real abelian number field F and for a prime p we study the relation between the p-parts of the class groups and of the quotients of global units modulo cyclotomic units along the cyclotomic p-extension of F. Assuming Greenberg's conjecture about the vanishing of the λ-invariant of the extension, a map between these groups has been constructed by several authors, and shown to be an isomorphism if p does not split in F. We focus in the split case, showing that there are, in general, non-trivial kernels and cokernels.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 148 , Issue 1 , January 2010 , pp. 93 - 106
Copyright
Copyright © Cambridge Philosophical Society 2009

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