On capitulations of even $K$-groups and pseudo-null submodules in $\mathbb{Z}_p^d$-extensions

Meng Fai Lim

On capitulations of even $K$-groups and pseudo-null submodules in $\mathbb{Z}_p^d$-extensions

Number Theory 2026-07-08 v1

Authors: Meng Fai Lim

Abstract

The capitulations of ideals in $\mathbb{Z}_p^d$ -extensions and pseudo-null submodules of the classical Iwasawa modules are closely related as evidenced in the works of Ozaki and Fujii. In this paper, we investigate the analogous situation for the even $K$ -groups. As an application, we obtain a new sufficient condition for existence of non-trivial pseudo-null submodules in the classical Iwasawa modules.

Keywords

capitulation even K-groups pseudo-null submodules Iwasawa modules Zp^d-extensions

Cite

@article{arxiv.2607.07328,
  title  = {On capitulations of even $K$-groups and pseudo-null submodules in $\mathbb{Z}_p^d$-extensions},
  author = {Meng Fai Lim},
  journal= {arXiv preprint arXiv:2607.07328},
  year   = {2026}
}

Comments

16 pages