2010/01/26 by Shou-Wu Zhang, Zhang, Shou-Wu
Mathematics · #Advanced Differential Equations and Dynamical Systems #Algebraic Geometry (math.AG) #FOS: Mathematics #Number Theory (math.NT)
paper · pdf · doi:10.48550/arxiv.1001.4788
openalex publication_date 2010/01/26 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
In this note, we show how the classical Hodge index theorem implies the Hodge index conjecture of Beilinson for height pairing of homologically trivial codimension two cycles over function field of characteristic 0. Such an index conjecture has been used in our paper on Gross-Schoen cycles to deduce the Bogomolov conjecture and a lower bound for Hodge class (or Faltings height) from some conjectures about metrized graphs which have just been recently proved by Zubeyir Cinkir.