Inequalities for semistable families of arithmetic varieties

Details Inequalities for semistable families of arithmetic varieties Inequalities for semistable families of arithmetic varieties

1997-10-07

arxiv.org/abs/alg-geom/9710007v3

Mathematics

Algebraic Geometry

Version 3.0 (75 pages), the new version of the paper titled "Relative Bogomolov's inequality in the arithmetic case"

Scientific paper

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.

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