Global pluripotential theory over a trivially valued field

Boucksom, Sébastien; Jonsson, Mattias

Annales de la Faculté des sciences de Toulouse : Mathématiques, Série 6, Tome 31 (2022) no. 3, pp. 647-836.

Nous développons une théorie du pluripotentiel global dans le contexte de la géométrie de Berkovich sur un corps trivialement valué. Plus précisément, nous définissons et étudions des fonctions et mesures d’énergie finie et un opérateur de Monge–Ampère non-archimédien sur toute variéte projective (éventuellement réductible). Nous explorons également la topologie de l’espace des valuations à croissance linéaire, et le comportement des fonctions plurisousharmoniques sur celui-ci.

We develop global pluripotential theory in the setting of Berkovich geometry over a trivially valued field. Specifically, we define and study functions and measures of finite energy and the non-Archimedean Monge–Ampère operator on any (possibly reducible) projective variety. We also investigate the topology of the space of valuations of linear growth, and the behavior of plurisubharmonic functions thereon.

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