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

نویسنده

  • Filippo A. E. Nuccio
چکیده

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 Zp-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. 2000 Mathematical Subject Classification: 11R23, 11R29

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تاریخ انتشار 2008