1997/10/07 by Shu Kawaguchi, Kawaguchi, Shu, Atsushi Moriwaki +1
Computer Science · Mathematics · #Advanced Differential Equations and Dynamical Systems #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #FOS: Mathematics #Polynomial and algebraic computation #alg-geom #math.AG
paper · pdf · doi:10.48550/arxiv.alg-geom/9710007
Version 3.0 (75 pages), the new version of the paper titled "Relative Bogomolov's inequality in the arithmetic case"
openalex publication_date 1997/10/07 · arxiv created 1998/03/03 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
In this paper, we will consider a generalization of Bogomolov's inequality and Cornalba-Harris-Bost's inequality to semistable families of arithmetic varieties under the idea that geometric semistability implies a certain kind of arithmetic positivity. The first one is an arithmetic analogue of the relative Bogomolov's inequality proved by the second author. We also establish the arithmetic Riemann-Roch formulae for stable curves over regular arithmetic varieties and generically finite morphisms of arithmetic varieties.