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

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 ${\mathbb{Z}}_p$-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.

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