English

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}
}
R2 v1 2026-07-22T16:33:58.633Z