Let be a polarized scheme over a Banach ring . We define and study a class of plurisubharmonic metrics on the Berkovich analytification . We focus mainly on the case where is a hybrid ring of power series, so that is the hybrid space associated to a degeneration of complex manifolds . We then prove that any plurisubharmonic metric on with logarithmic growth at zero admits a canonical plurisubharmonic extension to the hybrid space . We also discuss the continuity of the family of Monge-Ampère measures associated to a continuous plurisubharmonic hybrid metric.
Soit un schéma polarisé sur un anneau de Banach . Nous définissons et étudions la classe des métriques plurisousharmoniques sur l’analytifié de Berkovich . Nous nous intéressons en particulier au cas où est l’anneau hybride des séries convergentes, et est l’espace hybride associé à une dégénérescence de variétés complexes . Nous démontrons alors que toute métrique plurisousharmonique sur à croissance logarithmique en zéro admet une extension plurisousharmonique canonique à l’espace hybride . Nous discutons aussi de la continuité de la famille de mesures de Monge-Ampère associée à une métrique hybride plurisousharmonique continue.
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Keywords: Berkovich spaces, pluripotential theory, hybrid spaces
Mot clés : Espaces de Berkovich, théorie du pluripotentiel, espaces hybrides
Léonard Pille-Schneider 1
@article{JEP_2023__10__601_0, author = {L\'eonard Pille-Schneider}, title = {Global pluripotential theory on hybrid spaces}, journal = {Journal de l{\textquoteright}\'Ecole polytechnique {\textemdash} Math\'ematiques}, pages = {601--658}, publisher = {\'Ecole polytechnique}, volume = {10}, year = {2023}, doi = {10.5802/jep.228}, language = {en}, url = {https://jep.centre-mersenne.org/articles/10.5802/jep.228/} }
TY - JOUR AU - Léonard Pille-Schneider TI - Global pluripotential theory on hybrid spaces JO - Journal de l’École polytechnique — Mathématiques PY - 2023 SP - 601 EP - 658 VL - 10 PB - École polytechnique UR - https://jep.centre-mersenne.org/articles/10.5802/jep.228/ DO - 10.5802/jep.228 LA - en ID - JEP_2023__10__601_0 ER -
%0 Journal Article %A Léonard Pille-Schneider %T Global pluripotential theory on hybrid spaces %J Journal de l’École polytechnique — Mathématiques %D 2023 %P 601-658 %V 10 %I École polytechnique %U https://jep.centre-mersenne.org/articles/10.5802/jep.228/ %R 10.5802/jep.228 %G en %F JEP_2023__10__601_0
Léonard Pille-Schneider. Global pluripotential theory on hybrid spaces. Journal de l’École polytechnique — Mathématiques, Volume 10 (2023), pp. 601-658. doi : 10.5802/jep.228. https://jep.centre-mersenne.org/articles/10.5802/jep.228/
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