Wild coverings of Berkovich curves
Publications Mathématiques de Besançon (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 : 2017-11-30
DOI : https://doi.org/10.5802/pmb.18
Classification : 14E22,  11S15,  14G22
Mots clés: Berkovich geometry, wild ramification, different, Herbrand function
@article{PMB_2017____127_0,
     author = {Michael Temkin},
     title = {Wild coverings of Berkovich curves},
     journal = {Publications Math\'ematiques de Besan\c con},
     publisher = {Presses universitaires de Franche-Comt\'e},
     year = {2017},
     pages = {127-135},
     doi = {10.5802/pmb.18},
     zbl = {1428.14038},
     mrnumber = {3752490},
     language = {en},
     url = {pmb.centre-mersenne.org/item/PMB_2017____127_0/}
}
Michael Temkin. Wild coverings of Berkovich curves. Publications Mathématiques de Besançon (2017), pp. 127-135. doi : 10.5802/pmb.18. https://pmb.centre-mersenne.org/item/PMB_2017____127_0/

[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 1327.14117

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

[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 | Article | MR 3117171 | Zbl 1288.14014

[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 | Article | MR 3063898 | Zbl 1277.14020

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