La droite de Berkovich sur Z

Details La droite de Berkovich sur Z La droite de Berkovich sur Z

2008-09-17

arxiv.org/abs/0809.2880v1

Ast\'erisque n{\deg} 334 (2010)

Mathematics

Algebraic Geometry

379 pages, in French

Scientific paper

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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