Nakai–Moishezon Criterion for Adelic ℝ-Cartier Divisors

Abstract

Abstract We prove a Nakai–Moishezon criterion for adelic ${\mathbb {R}}$-Cartier divisors, which is an arithmetic analogue of a theorem of Campana and Peternell. Our main result answers a question of Burgos Gil, Philippon, Moriwaki, and Sombra. We deduce it from the case of adelic Cartier divisors (due to Zhang) by continuity arguments and reductions involving a generalization of Zhang’s theorem on successive minima.