On the arithmetic dynamics of monomial maps

On the arithmetic dynamics of monomial maps

We prove several results for the arithmetic dynamics of monomial maps, including Silverman’s conjectures on height growth, dynamical Mordell–Lang conjecture, and dynamical Manin–Mumford conjecture. These results were originally known for monomial maps on algebraic tori. We extend them to arbitrary t...

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Veröffentlicht in:Ergodic theory and dynamical systems 2019-12, Vol.39 (12), p.3388-3406
1. Verfasser: LIN, JAN-LI
Format: Artikel
Sprache:eng
Schlagworte:
Algebra
Arithmetic
Orbits
Original Article
Toruses
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Beschreibung
Zusammenfassung:We prove several results for the arithmetic dynamics of monomial maps, including Silverman’s conjectures on height growth, dynamical Mordell–Lang conjecture, and dynamical Manin–Mumford conjecture. These results were originally known for monomial maps on algebraic tori. We extend them to arbitrary toric varieties.
ISSN:0143-3857
1469-4417
DOI:10.1017/etds.2018.5