Smallness of Faltings heights of CM abelian varieties

DOI10.1016/j.jnt.2022.07.007OpenAlexW3211035703WikidataQ114156421 ScholiaQ114156421MaRDI QIDQ2079477

Xunjing Wei

Publication date: 30 September 2022

Published in: Journal of Number Theory (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/2111.00617

zbMATH Keywords

Siegel zeroArtin \(L\)-functionCM abelian varietiesColmez conjectureFaltings heightgood reduction of abelian varieties

Mathematics Subject Classification ID

Abelian varieties of dimension (> 1) (11G10) Complex multiplication and moduli of abelian varieties (11G15) (L)-functions of varieties over global fields; Birch-Swinnerton-Dyer conjecture (11G40) Heights (11G50) Arithmetic varieties and schemes; Arakelov theory; heights (14G40)

Cites Work

• Finiteness theorems for abelian varieties over number fields.
• Periods of abelian varieties with complex multiplication
• Some effective cases of the Brauer-Siegel theorem
• Faltings heights of abelian varieties with complex multiplication
• On the averaged Colmez conjecture
• On Colmez's product formula for periods of CM-Abelian varieties
• Introduction to modern number theory. Fundamental problems, ideas and theories. Transl. from the Russian
• Good reduction of abelian varieties
• Non-vanishing of \(L\)-functions and applications
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