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      La droite de Berkovich sur Z

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          Abstract

          We study here the Berkovich line over the ring of integers of a number field. It is a natural object which contains complex and non-Archimedean analytic spaces associated to each place. We prove that this line satisfies good topological and algebraic properties and exhibit a few examples of Stein spaces that lie in it. We derive applications to the study of convergent arithmetic power series: choice of zeroes and poles, noetherianity of global rings and inverse Galois problem. Typical examples of such power series are given by analytic functions on the open complex unit disk whose Taylor development in 0 has integer coefficients.

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          Rigid analytic spaces

          John Tate (1971)
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            Points de platitude d'un morphisme d'espaces analytiques complexes

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              Theorem A und Theorem B in der nichtarchimedischen Funktionentheorie

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                Author and article information

                Journal
                17 September 2008
                Article
                0809.2880
                238fb94e-eb47-4012-8901-15b9ee1009dd

                http://arxiv.org/licenses/nonexclusive-distrib/1.0/

                History
                Custom metadata
                14G22, 14G25 (Primary), 30B10, 13E05, 12F12 (Secondary)
                Ast\'erisque n{\deg} 334 (2010)
                379 pages, in French
                math.AG math.NT

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