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Variation de la dimension relative en géométrie analytique p-adique

Part of: Arithmetic problems. Diophantine geometry Algebraic geometry: Foundations

Published online by Cambridge University Press:  01 November 2007

Antoine Ducros
Antoine Ducros*
Affiliation:
Laboratoire J.-A. Dieudonné, Université de Nice – Sophia Antipolis, Parc Valrose, 06108 Nice cedex 02, France (email: [email protected])
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Abstract

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Let k be a complete, non-Archimedean valued field (the trivial absolute value is allowed) and let φ:X→Y be a morphism between two Berkovich k-analytic spaces; we show that, for any integer n, the set of points of X at which the local dimension of φ is at least equal to n is a Zariski-closed subset of X. In order to establish it, we first prove an analytic analogue of Zariski’s Main Theorem, and we also introduce, and study, the notion of an analytic system of parameters at a point.

Keywords

Berkovich analytic spacesdimension theory

MSC classification

Secondary: 14G22: Rigid analytic geometry 14A99: None of the above, but in this section
Type
Research Article
Information
Compositio Mathematica , Volume 143 , Issue 6 , November 2007 , pp. 1511 - 1532
Copyright
Copyright © Foundation Compositio Mathematica 2007