Rarity of pseudo-null Iwasawa modules for <i>p</i>-adic Lie extensions

Abstract In this article, we obtain a necessary and sufficient condition for the pseudo-nullity of the p -ramified Iwasawa module for p -adic Lie extensions 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.