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

Takenori Kataoka

doi:10.4153/S0008439525000037

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

Takenori Kataoka

Department of Mathematics

Research output: Contribution to journal › Article › peer-review

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.

Original language	English
Pages (from-to)	709-724
Number of pages	16
Journal	Canadian Mathematical Bulletin
Volume	68
Issue number	3
DOIs	https://doi.org/10.4153/S0008439525000037
Publication status	Published - 1 Sept 2025

Keywords

Greenberg’s generalized conjecture
Iwasawa modules
Iwasawa theory

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10.4153/S0008439525000037

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title = "Rarity of pseudo-null Iwasawa modules for p-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.",

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Y1 - 2025/9/1

N2 - 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.

AB - 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.

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KW - Iwasawa modules

KW - Iwasawa theory

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

Abstract

Keywords

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