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Covers in p-adic analytic geometry and log covers II: cospecialization of the (p′)-tempered fundamental group in higher dimensions

Part of: (Co)homology theory Arithmetic problems. Diophantine geometry

Published online by Cambridge University Press:  15 May 2012

Emmanuel Lepage
Emmanuel Lepage*
Affiliation:
D.M.A., E.N.S., 45 rue d’Ulm, 75005 Paris, France (email: [email protected])
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Abstract

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The tempered fundamental group of a p-adic variety classifies analytic étale covers that become topological covers for Berkovich topology after pullback by some finite étale cover. This paper constructs cospecialization homomorphisms between the (p′) versions of the tempered fundamental group of the fibers of a smooth morphism with polystable reduction. We study the question for families of curves in another paper. To construct them, we will start by describing the pro-(p′) tempered fundamental group of a smooth and proper variety with polystable reduction in terms of the reduction endowed with its log structure, thus defining tempered fundamental groups for log polystable varieties.

Keywords

fundamental groupsBerkovich spacesspecialization

MSC classification

Secondary: 14G22: Rigid analytic geometry 14F35: Homotopy theory; fundamental groups
Type
Research Article
Information
Compositio Mathematica , Volume 148 , Issue 5 , September 2012 , pp. 1443 - 1482
Copyright
Copyright © Foundation Compositio Mathematica 2012

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