The Chabauty space of ℚp×

Bourquin, Antoine; Valette, Alain

doi:10.2140/involve.2021.14.89

Download this article
	For screen
	For printing

Recent Issues

The Journal

Submission Guidelines

Submission Form

Policies for Authors

Ethics Statement

ISSN: 1944-4184 (e-only)

ISSN: 1944-4176 (print)

Author Index

Coming Soon

Other MSP Journals

This article is available for purchase or by subscription. See below.

The Chabauty space of $\mathbb{Q}_p^\times$

Antoine Bourquin and Alain Valette

Vol. 14 (2021), No. 1, 89–102

DOI: 10.2140/involve.2021.14.89

Abstract

Let $𝒞 (G)$ denote the Chabauty space of closed subgroups of the locally compact group $G$ . We first prove that $𝒞 (ℚ_{p}^{\times})$ is a proper compactification of $ℕ$ , identified with the set $N$ of open subgroups with finite index. Then we identify the space $𝒞 (ℚ_{p}^{\times}) \ N$ up to homeomorphism; e.g., for $p = 2$ , it is the Cantor space on which two copies of $\bar{N}$ (the 1-point compactification of $ℕ$ ) are glued.

PDF Access Denied

We have not been able to recognize your IP address 18.224.63.87 as that of a subscriber to this journal.
Online access to the content of recent issues is by subscription, or purchase of single articles.

Please contact your institution's librarian suggesting a subscription, for example by using our journal-recommendation form. Or, visit our subscription page for instructions on purchasing a subscription.

You may also contact us at contact@msp.org
or by using our contact form.

Or, you may purchase this single article for USD 30.00:

Keywords

Chabauty space, locally compact group, $p$-adic group, topological space, proper compactification

Mathematical Subject Classification 2010

Primary: 22B05, 54H11

Milestones

Received: 4 November 2019

Revised: 11 July 2020

Accepted: 15 September 2020

Published: 4 March 2021

Communicated by Kenneth S. Berenhaut

Authors

Antoine Bourquin
Institut de Mathématiques Université de Neuchâtel Neuchâtel Switzerland

Alain Valette
Faculté des Sciences Institut de Mathématiques Université de Neuchâtel Neuchâtel Switzerland

Vol. 14, No. 1, 2021