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Wild coverings of Berkovich curves
Publications mathématiques de Besançon. Algèbre et théorie des nombres (2017), pp. 127-135.

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.

Cet article est une version étendue de l’exposé de l’auteur à la conférence « Non-Archimedean analytic geometry : theory and practice » tenue à Papeete en août 2015. Il offre une vue d’ensemble des résultats et des méthodes des travaux récents [2] et [5] sur la structure des revêtements sauvages des courbes de Berkovich et sa relation avec la théorie de la différente et de la ramification supérieure.

Published online:
DOI: 10.5802/pmb.18
Classification: 14E22, 11S15, 14G22
Keywords: Berkovich geometry, wild ramification, different, Herbrand function
License: CC-BY-ND 4.0
Copyrights: The authors retain unrestricted copyrights and publishing rights 
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     author = {Michael Temkin},
     title = {Wild coverings of {Berkovich} curves},
     journal = {Publications math\'ematiques de Besan\c{c}on. Alg\`ebre et th\'eorie des nombres},
     pages = {127--135},
     publisher = {Presses universitaires de Franche-Comt\'e},
     year = {2017},
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Michael Temkin. Wild coverings of Berkovich curves. Publications mathématiques de Besançon. Algèbre et théorie des nombres (2017), pp. 127-135. doi : 10.5802/pmb.18. https://pmb.centre-mersenne.org/articles/10.5802/pmb.18/

[1] Omid Amini; Matthew Baker; Erwan Brugallé; Joseph Rabinoff Liting harmonic morphisms I: metrized complexes and Berkovich skeleta (2013) (https://arxiv.org/abs/1303.4812v3) | Zbl

[2] Adina Cohen; Michael Temkin; Dmitri Trushin Morphisms of Berkovich curves and the different function, Adv. Math., Volume 303 (2016), pp. 800-858 | DOI | MR | Zbl

[3] Xander Faber Topology and geometry of the Berkovich ramification locus for rational functions, I, Manuscr. Math., Volume 142 (2013) no. 3-4, pp. 439-474 | DOI | MR | Zbl

[4] Xander Faber Topology and geometry of the Berkovich ramification locus for rational functions, II, Math. Ann., Volume 356 (2013) no. 3, pp. 819-844 | DOI | MR | Zbl

[5] Michael Temkin Metric uniformization of morphisms of Berkovich curves, Adv. Math., Volume 317 (2017), pp. 438-472 | DOI | MR | Zbl

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