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VOL. 86 | 2020 Iwasawa invariants and linking numbers of primes
Yasushi Mizusawa, Gen Yamamoto

Editor(s) Masato Kurihara, Kenichi Bannai, Tadashi Ochiai, Takeshi Tsuji

Abstract

For an odd prime number $p$ and a number field $k$ which is an elementary abelian $p$-extension of the rationals, we prove the equivalence between the vanishing of all Iwasawa invariants of the cyclotomic $\mathbb{Z}_p$-extension of $k$ and an arithmetical condition described by the linking numbers of primes from a viewpoint of analogies between pro-$p$ Galois groups and link groups. A criterion of Greenberg's conjecture for $k$ of degree $p$ is also described in terms of linking matrices.

Information

Published: 1 January 2020
First available in Project Euclid: 12 January 2021

Digital Object Identifier: 10.2969/aspm/08610639

Subjects:
Primary: 11R23 (11R18)

Keywords: Arithmetic topology , Iwasawa invariants , linking numbers

Rights: Copyright © 2020 Mathematical Society of Japan

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