Abstract
In this paper, we will consider a generalization of Bogomolov’s inequality and Cornalba-Harris-Bost’s inequality to the case of 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 in [22]. We also establish the arithmetic Riemann-Roch formulae for stable curves over regular arithmetic varieties and generically finite morphisms of arithmetic varieties.
Citation
Shu Kawaguchi. Atsushi Moriwaki. "Inequalities for semistable families of arithmetic varieties." J. Math. Kyoto Univ. 41 (1) 97 - 182, 2001. https://doi.org/10.1215/kjm/1250517650
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