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April, 2020 $\mu$-type subgroups of $J_1(N)$ and application to cyclotomic fields
Masami OHTA
J. Math. Soc. Japan 72(2): 333-412 (April, 2020). DOI: 10.2969/jmsj/78327832

Abstract

Let $p$ be an odd prime number, and $N$ a positive integer prime to $p$. We prove that $\mu$-type subgroups of the modular Jacobian variety $J_1(N)$ or $J_1(Np)$ of order a power of $p$ and defined over some abelian extensions of $\mathbb{Q}$ are trivial, under several hypotheses. For the proof, we use the method of Vatsal. As application, we show that a conjecture of Sharifi is valid in some cases.

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Masami OHTA. "$\mu$-type subgroups of $J_1(N)$ and application to cyclotomic fields." J. Math. Soc. Japan 72 (2) 333 - 412, April, 2020. https://doi.org/10.2969/jmsj/78327832

Information

Received: 25 June 2017; Published: April, 2020
First available in Project Euclid: 20 February 2020

zbMATH: 07196907
MathSciNet: MR4090341
Digital Object Identifier: 10.2969/jmsj/78327832

Subjects:
Primary: 11G18
Secondary: 11R23, 14G05

Rights: Copyright © 2020 Mathematical Society of Japan

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Vol.72 • No. 2 • April, 2020
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