Given a Mumford curve over , we show that for every semistable model of and every closed point of this semistable model, there exists a finite étale cover of such that every semistable model of over has a vertical component above . We then give applications of this to the tempered fundamental group. In particular, we prove that two punctured Tate curves with isomorphic tempered fundamental groups are isomorphic over .
Cite this article
Emmanuel Lepage, Resolution of Nonsingularities for Mumford Curves. Publ. Res. Inst. Math. Sci. 49 (2013), no. 4, pp. 861–891DOI 10.4171/PRIMS/122