Resolution of non-singularities for Mumford curves

2011/11/22 by Emmanuel Lepage, Lepage, Emmanuel
Mathematics · #Algebraic Geometry (math.AG) #FOS: Mathematics #math.AG

paper · pdf · doi:10.48550/arxiv.1111.5342

arxiv created 2011/11/22 · arxiv updated 2011/11/24

Abstract

Given a Mumford curve X over \mathbb Q_p, we show that for every semistable model \mathcal X of X and every closed point x of this semistable model, there exists a finite étale cover Y of X such that every semistable model of Y has a vertical component above X. We then give applications of this to the tempered fundamental group. In particular, we prove that two punctured Tate curves \mathbb Q_p with isomorphic tempered fundamental groups are isomorphic over \mathbb Q_p.

Related

• Tempered fundamental group and metric graph of a Mumford curve
• Another proof of the Semistable Reduction Theorem
• Mumford curves and Mumford groups in positive characteristic
• On representations attached to semistable vector bundles on Mumford curves
• Measure-theoretic rigidity for Mumford curves