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

Part of: Algebraic number theory: global fields

Published online by Cambridge University Press:  10 January 2025

Takenori Kataoka
Takenori Kataoka*
Affiliation:
Department of Mathematics, Faculty of Science Division II, Tokyo University of Science, 1-3 Kagurazaka, Shinjuku-ku, Tokyo 162-8601, Japan
*
e-mail: tkataoka@rs.tus.ac.jp
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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.

Keywords

Iwasawa theoryIwasawa modulesGreenberg’s generalized conjecture

MSC classification

Primary: 11R23: Iwasawa theory
Type
Article
Information
Canadian Mathematical Bulletin , First View , pp. 1 - 16
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Copyright
© The Author(s), 2025. Published by Cambridge University Press on behalf of Canadian Mathematical Society

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Footnotes

This work is supported by JSPS KAKENHI (Grant No. 22K13898).

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