Cyclotomic Units and Class Groups in Z_p extensions of real abelian fields
Number Theory
2008-12-04 v1
Abstract
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.
Keywords
Cite
@article{arxiv.0812.0784,
title = {Cyclotomic Units and Class Groups in Z_p extensions of real abelian fields},
author = {Filippo A. E. Nuccio},
journal= {arXiv preprint arXiv:0812.0784},
year = {2008}
}
Comments
19 pages, part of the author's PhD thesis