The arithmetic Hodge index theorem for adelic line bundles II
Number Theory
2021-08-24 v2
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.
Keywords
Cite
@article{arxiv.1304.3539,
title = {The arithmetic Hodge index theorem for adelic line bundles II},
author = {Xinyi Yuan and Shou-Wu Zhang},
journal= {arXiv preprint arXiv:1304.3539},
year = {2021}
}
Comments
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