Publications Mathématiques de Besançon
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Walter Gubler; Julius Hertel
Local Heights of Toric Varieties over Non-archimedean Fields
(Hauteurs locales des variétés toriques sur un corps ultramétrique complet)
Publications mathématiques de Besançon (2017), p. 5-77
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Class. Math.: 14M25, 14G40, 14G22
Mots clés: Toric geometry, local heights, berkovich spaces, Chambert-Loir measure, heights of varieties over finitely generated fields

Résumé

Nous généralisons des résultats concernant les hauteurs locales prouvés précédemment pour une valuation discrète au cas d’une valeur absolue ultramétrique quelconque. Nous traitons tout d’abord le case de la formule de récurrence de Chambert-Loir et Thuillier. Ensuite nous généralisons la formule de Burgos–Philippon–Sombra pour la hauteur locale torique d’une variété torique normale propre. Nous appliquons la formule correspondante de Moriwaki pour les hauteurs globales sur un corps de type fini au cas d’une fibration qui est génériquement torique. Nous illustrons ce dernier résultat par un exemple naturel où des valuations non discrètes jouent un rôle important.

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