Greenberg's conjecture and units in multiple Z_p-extensions
Number Theory
2007-05-23 v1
Abstract
In this paper we prove Greenberg's pseudo-null conjecture for the field of p-th roots of unity in the case that p exactly divides the class number and the index of the global units in the local units. We also generalize to the case of multiple Z_p-extensions a theorem of Iwasawa on the Kummer extension of the cyclotomic Z_p-extension generated by p-power roots of units .
Keywords
Cite
@article{arxiv.math/0007209,
title = {Greenberg's conjecture and units in multiple Z_p-extensions},
author = {William G. McCallum},
journal= {arXiv preprint arXiv:math/0007209},
year = {2007}
}