Coverings in p-adic analytic geometry and log coverings I: Cospecialization of the (p')-tempered fundamental group for a family of curves

2009/09/15 by Emmanuel Lepage, Lepage, Emmanuel · 1 citation
Computer Science · Mathematics · #11G20 #14G22 #14H30 #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #FOS: Mathematics #Topological and Geometric Data Analysis #advanced mathematical theories

paper · pdf · doi:10.48550/arxiv.0909.2805

openalex publication_date 2009/09/15 · openalex created_date 2016/06/24 · openalex updated_date 2026/07/28

Abstract

The tempered fundamental group of a p-adic analytic space classifies coverings that are dominated by a topological covering (for the Berkovich topology) of a finite etale covering of the space. Here we construct cospecialization homomorphisms between (p') versions of the tempered fundamental groups of the fibers of a smooth family of curves with semistable reduction. To do so, we will translate our problem in terms of cospecialization morphisms of fundamental groups of the log fibers of the log reduction. In particular, we will have to study invariance of the geometric log fundamental group of saturated log smooth log schemes over a log point by change of log point.

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• Families of curves separating points

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