Rarity of pseudo-null Iwasawa modules for $p$-adic Lie extensions

Takenori Kataoka

Rarity of pseudo-null Iwasawa modules for $p$-adic Lie extensions

Number Theory 2024-07-15 v1

Authors: Takenori Kataoka

Abstract

In this paper, we obtain a necessary and sufficient condition for the pseudo-nullity of the $p$ -ramified Iwasawa module for $p$ -adic Lie extension of totally real fields. It is applied to answer the corresponding question for the minus component of the unramified Iwasawa module for CM-fields. The results show that the pseudo-nullity is very rare.

Keywords

pseudo-null Iwasawa module $p$-adic Lie extension totally real fields CM-fields ramification

Cite

@article{arxiv.2407.09002,
  title  = {Rarity of pseudo-null Iwasawa modules for $p$-adic Lie extensions},
  author = {Takenori Kataoka},
  journal= {arXiv preprint arXiv:2407.09002},
  year   = {2024}
}

Comments

14 pages

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