JournalsprimsVol. 49, No. 4pp. 861–891

Resolution of Nonsingularities for Mumford Curves

  • Emmanuel Lepage

    Université Pierre et Marie Curie VI, Paris, France
Resolution of Nonsingularities for Mumford Curves cover
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Abstract

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

Cite this article

Emmanuel Lepage, Resolution of Nonsingularities for Mumford Curves. Publ. Res. Inst. Math. Sci. 49 (2013), no. 4, pp. 861–891

DOI 10.4171/PRIMS/122