Tempered fundamental group and metric graph of a Mumford curve

Details Tempered fundamental group and metric graph of a Mumford curve Tempered fundamental group and metric graph of a Mumford curve

2008-11-19

arxiv.org/abs/0811.3169v1

Mathematics

Algebraic Geometry

39 pages

Scientific paper

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.

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