Geodesic
Characterisation of the Berkovich spectrum of the Banach algebra of bounded continuous functions
Documenta mathematica, Tome 19 (2014), pp. 769-799.

Voir la notice de l'article provenant de la source Electronic Library of Mathematics

Summary: For a complete valuation field $k$ and a topological space $X$, we prove the universality of the underlying topological space of the Berkovich spectrum of the Banach $k$-algebra $\m{C}_{\m{bd}}(X,k)$ of bounded continuous $k$-valued functions on $X$. This result yields three applications: a partial solution to an analogue of Kaplansky conjecture for the automatic continuity problem over a local field, comparison of two ground field extensions of $\m{C}_{\m{bd}}(X,k)$, and non-Archimedean Gel'fand theory.
Classification : 11S80, 18B30, 46S10
Keywords: berkovich spectrum, stone space, banaschewski compactification, non-Archimedean Gelfand--Naimark theorem, non-Archimedean Gelfand theory, non-Archimedean Kaplansky conjecture 
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     author = {Mihara, Tomoki},
     title = {Characterisation of the {Berkovich} spectrum of the {Banach} algebra of bounded continuous functions},
     journal = {Documenta mathematica},
     pages = {769--799},
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     volume = {19},
     year = {2014},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/DOCMA_2014__19__a20/}
}
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Mihara, Tomoki. Characterisation of the Berkovich spectrum of the Banach algebra of bounded continuous functions. Documenta mathematica, Tome 19 (2014), pp. 769-799. http://geodesic.mathdoc.fr/item/DOCMA_2014__19__a20/