On 2-adic Lie Iterated Extensions of Number Fields Arising from a Joukowski Map

Abstract

We construct a special $2$-adic Lie extension of a number field as an iterated tower by a conjugate of Joukowski map. If the number field is totally real, the unramified Iwasawa module over such a $2$-adic Lie iterated extension is conjecturally pseudo-null under Greenberg's conjecture for all intermediate cyclotomic $\mathbb{Z}_2$-extensions. We give some examples of such $2$-adic Lie iterated extensions with pseudo-null Iwasawa modules.