July 12, 2024Open Access

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

TKTakenori KataokaTokyo University of Science

Key Points

Key points are not available for this paper at this time.

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.

Demander à l'IA

Bookmark

View Full Paper

Cite This Study

Takenori Kataoka (Fri,) studied this question.

synapsesocial.com/papers/68e6087cb6db64358759c425 https://doi.org/https://doi.org/10.48550/arxiv.2407.09002

Also Consider

Synapse has enriched 5 closely related papers on similar clinical questions. Consider them for comparative context:

1Minimal resolutions of Iwasawa modules2024
2On the triviality of the unramified Iwasawa modules of the maximal multiple $\mathbb{Z}_p$-extensions2024
3A note on extensions of <i>p</i> -adic representations of upper G upper L Subscript 2 Baseline left parenthesis upper Q Subscript p Baseline right parenthesis$\mathrm {GL}_2(\mathbb {Q}_p)$ <mml:math xmlns:xlink="http://www.w3.org/1999/xlink" xmlns:mnf="http://cambridge.org/core/manifest" xmlns:cup="http://contentservices.cambridge.org" xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:m="http://cambridge.org/core/metadata" xmlns:core="http://cambridge.org/core" xmlns:c="http://cambridge.org/core/content" display="inline"> <mml:mrow> <mml:mstyle mathvariant="normal"> <mml:msub> <mml:mrow> <mml:mi>G</mml:mi> <mml:mi>L</mml:mi> </mml:mrow> <mml:mn>2</mml:mn> </mml:msub> </mml:mstyle> <mml:mo stretchy="false" form="prefix" fence="true">(</mml:mo> <mml:mstyle mathvariant="double-struck"> <mml:msub> <mml:mi>Q</mml:mi> <mml:mi>p</mml:mi> </mml:msub> </mml:mstyle> <mml:mo stretchy="false" form="postfix" fence="true">)</mml:mo> </mml:mrow> </mml:math>2026
4On $$\mathbb {Z}_2$$-extensions of real quadratic fields with four odd ramified prime numbers2026
5Unramified Iwasawa module of $\mathbb{Z}_2$-extension of certain quadratic fields with a bounded quotient2024

Demander à l'IA

Bookmark

View Full Paper