Energy Minimization Principle for non-archimedean curves
Veronika Wanner1
1 Mathematik, Universität Regensburg 93040 Regensburg, Germany
Journal de théorie des nombres de Bordeaux, Volume 34 (2022) no. 1, pp. 1-39.

Baker and Rumely defined a notion of Arakelov–Green’s functions on the Berkovich analytification of the projective line and established an Energy Minimization Principle. We extend their definition and show their Energy Minimization Principle for general smooth projective curves. As an application we get a generalization and a different proof of an equidistribution result by Baker and Petsche.

Baker et Rumely ont défini la notion de fonction d’Arakelov–Green sur la droite projective analytifiée au sens de Berkovich et ont établi un principe de minimisation de l’énergie pour ces fonctions. Nous étendons leur définition et démontrons leur principe de minimisation de l’énergie pour les courbes projectives lisses générales. Comme application, nous obtenons une généralisation et une nouvelle démonstration d’un résultat d’équidistribution de Baker et Petsche.

Received:
Revised:
Accepted:
Published online:
DOI: 10.5802/jtnb.1192
Classification: 32P05, 14G22, 14T05, 32U05, 32U40
Keywords: Potential theory, Berkovich spaces, Equidistribution
Veronika Wanner 1

1 Mathematik, Universität Regensburg 93040 Regensburg, Germany
License: CC-BY-ND 4.0
Copyrights: The authors retain unrestricted copyrights and publishing rights 
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Veronika Wanner. Energy Minimization Principle for non-archimedean curves. Journal de théorie des nombres de Bordeaux, Volume 34 (2022) no. 1, pp. 1-39. doi : 10.5802/jtnb.1192. https://jtnb.centre-mersenne.org/articles/10.5802/jtnb.1192/

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