A consequence of Greenberg's generalized conjecture on Iwasawa invariants of $\mathbb{Z}_p$-extensions

Takenori Kataoka

A consequence of Greenberg's generalized conjecture on Iwasawa invariants of $\mathbb{Z}_p$-extensions

Number Theory 2016-11-01 v1

Authors: Takenori Kataoka

Abstract

For a prime number $p$ and a number field $k$ , let $\tilde{k}$ be the compositum of all $\mathbb{Z}_p$ -extensions of $k$ . Greenberg's Generalized Conjecture (GGC) claims the pseudo-nullity of the unramified Iwasawa module $X(\tilde{k})$ of $\tilde{k}$ . It is known that, when $k$ is an imaginary quadratic field, GGC has a consequence on the Iwasawa invariants associated to $\mathbb{Z}_p$ -extensions of $k$ . In this paper, we partially generalize it to arbitrary number fields $k$ .

Keywords

iwasawa invariants greenberg's generalized conjecture z_p-extensions number fields pseudo-nullity unramified iwasawa module imaginary quadratic fields

Cite

@article{arxiv.1602.07916,
  title  = {A consequence of Greenberg's generalized conjecture on Iwasawa invariants of $\mathbb{Z}_p$-extensions},
  author = {Takenori Kataoka},
  journal= {arXiv preprint arXiv:1602.07916},
  year   = {2016}
}

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28 pages

A consequence of Greenberg's generalized conjecture on Iwasawa invariants of $\mathbb{Z}_p$-extensions

Abstract

Keywords

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