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

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.

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.

Publié le :
DOI : https://doi.org/10.5802/pmb.18
Classification : 14E22,  11S15,  14G22
Mots clés : Berkovich geometry, wild ramification, different, Herbrand function
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     author = {Temkin, Michael},
     title = {Wild coverings of {Berkovich} curves},
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Temkin, Michael. Wild coverings of Berkovich curves. Publications mathématiques de Besançon. Algèbre et théorie des nombres (2017), pp. 127-135. doi : 10.5802/pmb.18. http://archive.numdam.org/articles/10.5802/pmb.18/

[1] Amini, Omid; Baker, Matthew; Brugallé, Erwan; Rabinoff, Joseph Liting harmonic morphisms I: metrized complexes and Berkovich skeleta (2013) (https://arxiv.org/abs/1303.4812v3) | Zbl 1327.14117

[2] Cohen, Adina; Temkin, Michael; Trushin, Dmitri Morphisms of Berkovich curves and the different function, Adv. Math., Volume 303 (2016), pp. 800-858 | Article | MR 3552539 | Zbl 06636658

[3] Faber, Xander Topology and geometry of the Berkovich ramification locus for rational functions, I, Manuscr. Math., Volume 142 (2013) no. 3-4, pp. 439-474 | Article | MR 3117171 | Zbl 1288.14014

[4] Faber, Xander Topology and geometry of the Berkovich ramification locus for rational functions, II, Math. Ann., Volume 356 (2013) no. 3, pp. 819-844 | Article | MR 3063898 | Zbl 1277.14020

[5] Temkin, Michael Metric uniformization of morphisms of Berkovich curves, Adv. Math., Volume 317 (2017), pp. 438-472 | Article | MR 3682674 | Zbl 1401.14132

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