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International audienceFor 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

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

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