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Wild ramification kinks

Authors
  • Obus, Andrew1
  • Wewers, Stefan2
  • 1 University of Virginia, Department of Mathematics, Charlottesville, VA, USA , Charlottesville (United States)
  • 2 Universität Ulm, Institut für Reine Mathematik, Ulm, Germany , Ulm (Germany)
Type
Published Article
Journal
Research in the Mathematical Sciences
Publisher
Springer International Publishing
Publication Date
Oct 01, 2016
Volume
3
Issue
1
Identifiers
DOI: 10.1186/s40687-016-0070-0
Source
Springer Nature
Keywords
License
Green

Abstract

Given a branched cover f:Y→X\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$f{:}\,Y\rightarrow X$$\end{document} between smooth projective curves over a non-archimedean mixed-characteristic local field and an open rigid disk D⊂X\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$D\subset X$$\end{document}, we study the question under which conditions the inverse image f-1(D)\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$f^{-1}(D)$$\end{document} is again an open disk. More generally, if the cover f varies in an analytic family, is this true at least for some member of the family? Our main result gives a criterion for this to happen.

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