Cyclotomic Units and Class Groups in Z_p-extensions of real abelian number fields

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 Z_p-extension of F. Assuming Greenberg's conjecture about the van- ishing 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.
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Contributor : Filippo A. E. Nuccio Mortarino Majno Di Capriglio <>
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Filippo Alberto Edoardo Nuccio Mortarino Majno Di Capriglio. Cyclotomic Units and Class Groups in Z_p-extensions of real abelian number fields. Mathematical Proceedings, Cambridge University Press (CUP), 2009, 148, pp.93-106. ⟨10.1017/S0305004109990119⟩. ⟨hal-00947151⟩

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