Reports on families of imaginary abelian fields with pseudo-null unramified Iwasawa modules

TL;DR

This paper constructs an infinite family of imaginary abelian fields with non-trivial, pseudo-null Iwasawa modules in their maximal multiple Z_p-extensions, and explores implications for non-abelian Iwasawa theory.

Contribution

It demonstrates the existence of infinite families of imaginary abelian fields with specific Iwasawa module properties, advancing understanding in Iwasawa theory.

Findings

Existence of infinite families with pseudo-null Iwasawa modules

Non-triviality of Iwasawa modules in these fields

Applications to non-abelian Iwasawa theory

Abstract

Let $p$ be a prime number. We show that, there exists an infinite family of imaginary abelian fields such that, the Iwasawa module of the maximal multiple ${\Bbb Z}_p$-extension is non trivial and pseudo-null for each field in the family. We also discuss on an application to non-abelian Iwasawa theory in the sense of Ozaki.