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Arithmetic and dynamical degrees of self-morphisms of semi-abelian varieties

Part of: Arithmetic and non-Archimedean dynamical systems

Published online by Cambridge University Press:  17 October 2018

YOHSUKE MATSUZAWA  and
KAORU SANO
YOHSUKE MATSUZAWA
Affiliation:
Graduate School of Mathematical Sciences, The University of Tokyo, Komaba, Tokyo, 153-8914, Japan email myohsuke@ms.u-tokyo.ac.jp
KAORU SANO
Affiliation:
Department of Mathematics, Faculty of Science, Kyoto University, Kyoto 606-8502, Japan email ksano@math.kyoto-u.ac.jp
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Abstract

We prove a conjecture by Kawaguchi–Silverman on arithmetic and dynamical degrees, for self-morphisms of semi-abelian varieties. Moreover, we determine the set of the arithmetic degrees of orbits and the (first) dynamical degrees of self-morphisms of semi-abelian varieties.

Keywords

arithmeticalgebraic dynamicsHeightssemi-abelian vareitiesdynamical degree

MSC classification

Primary: 37P30: Height functions; Green functions; invariant measures
Secondary: 37P55: Arithmetic dynamics on general algebraic varieties
Type
Original Article
Information
Ergodic Theory and Dynamical Systems , Volume 40 , Issue 6 , June 2020 , pp. 1655 - 1672
Copyright
© Cambridge University Press, 2018

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