Vol. 14, No. 1, 2021

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

Antoine Bourquin and Alain Valette

Vol. 14 (2021), No. 1, 89–102

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

Chabauty space, locally compact group, $p$-adic group, topological space, proper compactification
Mathematical Subject Classification 2010
Primary: 22B05, 54H11
Received: 4 November 2019
Revised: 11 July 2020
Accepted: 15 September 2020
Published: 4 March 2021

Communicated by Kenneth S. Berenhaut
Antoine Bourquin
Institut de Mathématiques
Université de Neuchâtel
Alain Valette
Faculté des Sciences
Institut de Mathématiques
Université de Neuchâtel