Dynamical canonical heights for Jordan blocks, arithmetic degrees of orbits, and nef canonical heights on abelian varieties

DOI10.1090/tran/6596zbMath1391.37078arXiv1301.4964OpenAlexW2221258306WikidataQ56987132 ScholiaQ56987132MaRDI QIDQ2790646

Shu Kawaguchi, Joseph H. Silverman

Publication date: 7 March 2016

Published in: Transactions of the American Mathematical Society (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1301.4964

zbMATH Keywords

abelian varietycanonical heightarithmetic degreenef divisor

Mathematics Subject Classification ID

Abelian varieties of dimension (> 1) (11G10) Heights (11G50) Arithmetic dynamics on general algebraic varieties (37P55) Height functions; Green functions; invariant measures in arithmetic and non-Archimedean dynamical systems (37P30) Dynamical systems over global ground fields (37P15)

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Cites Work

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• Factorization of matrices of quaternions
• Erratum to ``On the dynamical and arithmetic degrees of rational self-maps of algebraic varieties
• Examples of dynamical degree equals arithmetic degree
• Canonical Vector Heights on Algebraic K3 Surfaces with Picard Number Two
• Dynamical degree, arithmetic entropy, and canonical heights for dominant rational self-maps of projective space
• Linear Transformations with Invariant Cones

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