Rarity of pseudo-null Iwasawa modules for $p$-adic Lie extensions

Takenori Kataoka

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arXiv · 2407.09002

Rarity of pseudo-null Iwasawa modules for $p$-adic Lie extensions

Takenori Kataoka

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Abstract

In this paper, we obtain a necessary and sufficient condition for the pseudo-nullity of the $p$-ramified Iwasawa module for $p$-adic Lie extension 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.

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Takenori Kataoka. 2024-07-12. Rarity of pseudo-null Iwasawa modules for $p$-adic Lie extensions. https://arxiv.org/abs/2407.09002

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