The arithmetic Hodge index theorem for adelic line bundles I

2013/04/12 by Xinyi Yuan, Yuan, Xinyi, Shou-Wu Zhang +1 · 3 citations
Mathematics · #Algebraic Geometry and Number Theory #Geometry and complex manifolds #Advanced Algebra and Geometry

paper · pdf · doi:10.48550/arxiv.1304.3538

Abstract

This is the first paper of a series. We prove an arithmetic Hodge index theorem for adelic line bundles on projective varieties over number fields. It extends the arithmetic Hodge index theorem of Faltings, Hriljac and Moriwaki on arithmetic varieties. As consequences, we obtain the uniqueness part of the non-archimedean Calabi--Yau theorem, and a rigidity property of the sets of preperiodic points of polarizable algebraic dynamical systems over number fields.

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• On the centralizers of endomorphisms of the projective line
• A quantitative dynamical Zhang fundamental inequality and Bogomolov-type problems
• Geometric Bogomolov conjecture for semiabelian varieties

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