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On the number of connected components of the ramification locus of a morphism of Berkovich curves

Authors
  • Bojković, Velibor1
  • Poineau, Jérôme2
  • 1 Universita di Padova, Dipartimento di matematica Tullio Levi-Civita, Via Trieste 63, Padova, 35121, Italy , Padova (Italy)
  • 2 Université de Caen, Laboratoire de mathématiques Nicolas Oresme, Caen Cedex, 14032, France , Caen Cedex (France)
Type
Published Article
Journal
Mathematische Annalen
Publisher
Springer Berlin Heidelberg
Publication Date
Mar 14, 2018
Volume
372
Issue
3-4
Pages
1575–1595
Identifiers
DOI: 10.1007/s00208-018-1668-x
Source
Springer Nature
Keywords
License
Yellow

Abstract

Let k be a complete nontrivially valued non-archimedean field. Given a finite morphism of quasi-smooth k-analytic curves that admit finite triangulations, we provide upper bounds for the number of connected components of the ramification locus in terms of topological invariants of the source curve such as its topological genus, the number of points in the boundary and the number of open ends.

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