2025/07/14 by Jackson S. Morrow, Morrow, Jackson S.
Mathematics · #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #FOS: Mathematics #Geometry and complex manifolds #Meromorphic and Entire Functions #Number Theory (math.NT)
paper · pdf · doi:10.48550/arxiv.2507.10410
openalex publication_date 2025/07/14 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
In this work, we relate recent work of Yuan--Zhang and Song on adelic line bundles over quasi-projective arithmetic varieties to recent advances in pluripotential theory on global Berkovich spaces from Pille-Schneider. In particular, we establish an equivalence between subcategories of adelic line bundles on quasi-projective varieties and line bundles on their Berkovich analytifications equipped with a continuous plurisubharmonic metric. We also provide several applications of this equivalence. For example, we generalize a construction of Pille-Schneider concerning families of Monge--Ampère measures on analytifications of projective arithmetic varieties to the quasi-projective setting. With this construction, we offer a new description of non-degenerate subvarieties which involves Monge--Ampère measures over trivially valued fields. Finally, we define a Monge--Ampère measure on the analytification of a quasi-projective arithmetic variety.