2008/11/19 by Emmanuel Lepage, Lepage, Emmanuel
Computer Science · Mathematics · #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #Commutative Algebra and Its Applications #FOS: Mathematics #Topological and Geometric Data Analysis #math.AG
paper · pdf · doi:10.48550/arxiv.0811.3169
39 pages
arxiv created 2008/11/19 · openalex publication_date 2008/11/19 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
This paper is an attempt to give some general results on the tempered fundamental group of a p-adic smooth algebraic varieties (which is a sort of analog of the topologic fundamental group of complex algebraic varieties in the p-adic world). The main result asserts that one can recover the metric structure of the graph of the stable model of a Mumford curve from the tempered fundamental group of this Mumford curve. We will also prove birational invariance, invariance by algebraically closed extensions and a Kuenneth formula for the tempered fundamental group. We will describe the tempered fundamental group of an abelian variety and link the tempered fundamental group of a curve to the tempered fundamental group of its Jacobian variety.