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Volume 46, Issue 4, 2010, pp. 849–897
DOI: 10.2977/PRIMS/28

Published online: 2010-11-18

Tempered Fundamental Group and Metric Graph of a Mumford Curve

Emmanuel Lepage[1]

(1) Université Pierre et Marie Curie VI, Paris, France

The aim of this paper is to give some general results on the tempered fundamental group of p-adic smooth algebraic varieties (which is a sort of analog of the topological 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 the curve. We also prove the birational invariance, invariance under algebraically closed extensions and a Kunneth formula for the tempered fundamental group. We 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.

Keywords: p-adic fundamental groups, Berkovich geometry

Lepage Emmanuel: Tempered Fundamental Group and Metric Graph of a Mumford Curve. Publ. Res. Inst. Math. Sci. 46 (2010), 849-897. doi: 10.2977/PRIMS/28