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arXiv · 0811.3169

Tempered fundamental group and metric graph of a Mumford curve

Emmanuel Lepage
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Abstract

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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Emmanuel Lepage. 2008-11-19. Tempered fundamental group and metric graph of a Mumford curve. https://arxiv.org/abs/0811.3169

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