The arithmetic Hodge index theorem for adelic line bundles II

Abstract

This is the second paper of a series. It extends the results of the first paper from number fields to finitely generated fields, based on the recent theory of adelic line bundles of the same authors. We prove an arithmetic Hodge index theorem for these adelic line bundles, and apply the theorem to obtain a rigidity property of the sets of preperiodic points of polarizable algebraic dynamical systems over any field.

The original version (arXiv:1304.3539v1) published in 2013 has been divided into two papers: a paper (arXiv:2105.13587) addressing the theory of adelic line bundles and the current new version (arXiv:1304.3539v2) addressing the Hodge index theorem for adelic line bundles

References in corpus (2)

• Questions on self maps of algebraic varieties
• A dynamical pairing between two rational maps

Cited by in corpus (6)

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• The Dynamical Manin-Mumford Conjecture and the Dynamical Bogomolov Conjecture for split rational maps
• Heights and arithmetic dynamics over finitely generated fields
• Canonical Kahler metrics and Arithmetics -- Generalising Faltings heights
• Some problems of arithmetic origin in rational dynamics
• On the concavity of the arithmetic volumes