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The Chabauty
space of $\mathbb{Q}_p^\times$
Antoine Bourquin and Alain Valette
Vol. 14 (2021), No. 1, 89–102
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Abstract |
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Let denote the Chabauty space of closed subgroups of the locally compact group . We first prove that is a proper compactification of , identified with the set of open subgroups with finite index. Then we identify the space up to homeomorphism; e.g., for , it is the Cantor space on which two copies of (the 1-point compactification of ) are glued. |
Keywords
Chabauty space, locally compact group, $p$-adic group,
topological space, proper compactification
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Mathematical Subject Classification 2010
Primary: 22B05, 54H11
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Milestones
Received: 4 November 2019
Revised: 11 July 2020
Accepted: 15 September 2020
Published: 4 March 2021
Communicated by Kenneth S. Berenhaut
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Authors |
| Antoine Bourquin | |
| Institut de Mathématiques Université de Neuchâtel Neuchâtel Switzerland |
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| Alain Valette | |
| Faculté des Sciences Institut de Mathématiques Université de Neuchâtel Neuchâtel Switzerland |
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