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

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

2008-12-03

arxiv.org/abs/0812.0784v1

Mathematics

Number Theory

19 pages, part of the author's PhD thesis

Scientific paper

For a real abelian field and for an odd prime p splitting in the field, we study a map between the p-parts of the class group and of the quotient of units modulo Cyclotomic Units, respectively, along the cyclotomic Z_p-extension of the field. We determine the kernel and the cokernel of this map assuming Greenberg's conjecture on the vanishing of the lambda-invariant of the extension.

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