Journal of Mathematics of Kyoto University

Inequalities for semistable families of arithmetic varieties

Shu Kawaguchi and Atsushi Moriwaki

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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.

Article information

J. Math. Kyoto Univ., Volume 41, Number 1 (2001), 97-182.

First available in Project Euclid: 17 August 2009

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 14G40: Arithmetic varieties and schemes; Arakelov theory; heights [See also 11G50, 37P30]
Secondary: 11G35: Varieties over global fields [See also 14G25] 11G50: Heights [See also 14G40, 37P30]


Kawaguchi, Shu; Moriwaki, Atsushi. Inequalities for semistable families of arithmetic varieties. J. Math. Kyoto Univ. 41 (2001), no. 1, 97--182. doi:10.1215/kjm/1250517650.

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