Publications Mathématiques de Besançon
Algèbre et Théorie des Nombres
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Michael Temkin
Wild coverings of Berkovich curves
Publications mathématiques de Besançon (2017), p. 127-135, doi: 10.5802/pmb.18
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Class. Math.: 14E22, 11S15, 14G22
Keywords: Berkovich geometry, wild ramification, different, Herbrand function

Abstract

This paper is an extended version of the author’s talk given at the conference “Non-Archimedean analytic geometry: theory and practice” held in August 2015 at Papeete. It gives a brief overview of results and methods of recent works [2] and [5] on the structure of wild coverings of Berkovich curves and its relation to the different and higher ramification theory.

Bibliography

[1] Omid Amini, Matthew Baker, Erwan Brugallé & Joseph Rabinoff, “Liting harmonic morphisms I: metrized complexes and Berkovich skeleta”, https://arxiv.org/abs/1303.4812v3, 2013
[2] Adina Cohen, Michael Temkin & Dmitri Trushin, “Morphisms of Berkovich curves and the different function”, Adv. Math. 303 (2016), p. 800-858 Article
[3] Xander Faber, “Topology and geometry of the Berkovich ramification locus for rational functions, I”, Manuscr. Math. 142 (2013) no. 3-4, p. 439-474 Article
[4] Xander Faber, “Topology and geometry of the Berkovich ramification locus for rational functions, II”, Math. Ann. 356 (2013) no. 3, p. 819-844 Article
[5] Michael Temkin, “Metric uniformization of morphisms of Berkovich curves”, Adv. Math. 317 (2017), p. 438-472

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