A local version of the arithmetic Hodge index theorem over quasiprojective varieties

2025/03/18 by Abboud, Marc
#14G40 #32P05 #32W20 #Algebraic Geometry (math.AG) #FOS: Mathematics #Number Theory (math.NT)

paper · doi:10.48550/arxiv.2503.14099

Abstract

We define a local intersection number for metrised line bundles over quasiprojective varieties with compact support and show the local arithmetic Hodge index theorem for this intersection number. As a consequence we obtain a uniqueness result for the Monge-Ampère equation over quasiprojective varieties within a certain class of solutions both in the archimedean and non-archimedean setting.

Related

• The arithmetic Hodge index theorem for adelic line bundles I
• Intersection pairing for arithmetic cycles with degenerate Green currents
• Complex Monge-Ampère equations on quasi-projective varieties
• Hodge Theory of p-adic varieties: a survey
• On the non-abelian Hodge locus I