2021/05/10 by Jackson S. Morrow, Giovanni Rosso, Morrow, Jackson S. +1
Mathematics · #14G05 #14G22 #26E30 #32Q45 #Advanced Topology and Set Theory #Algebraic Geometry (math.AG) #FOS: Mathematics #Functional Equations Stability Results #Number Theory (math.NT) #advanced mathematical theories
paper · pdf · doi:10.48550/arxiv.2105.04352
openalex publication_date 2021/05/10 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Let K be an algebraically closed, complete, non-Archimedean valued field of characteristic zero, and let \mathscrX be a K-analytic space (in the sense of Huber). In this work, we pursue a non-Archimedean characterization of Campana's notion of specialness. We say \mathscrX is K-analytically special if there exists a connected, finite type algebraic group G/K, a dense open subset \mathscrU⊂ Gan with codim(Gan∖ \mathscrU) ≥ 2, and an analytic morphism \mathscrU → \mathscrX which is Zariski dense. With this definition, we prove several results which illustrate that this definition correctly captures Campana's notion of specialness in the non-Archimedean setting. These results inspire us to make non-Archimedean counterparts to conjectures of Campana. As preparation for our proofs, we prove auxiliary results concerning the indeterminacy locus of a meromorphic mapping between K-analytic spaces, the notion of pseudo-K-analytically Brody hyperbolic, and extensions of meromorphic maps from smooth, irreducible K-analytic spaces to the analytification of a semi-abelian variety.