1. On the arithmetic dynamics of monomial maps
- Author
-
Jan-Li Lin
- Subjects
Monomial ,Pure mathematics ,Conjecture ,Mathematics - Number Theory ,Mathematics::Commutative Algebra ,Mathematics::Number Theory ,Applied Mathematics ,General Mathematics ,010102 general mathematics ,Torus ,Dynamical Systems (math.DS) ,Arithmetic dynamics ,01 natural sciences ,Mathematics - Algebraic Geometry ,Mathematics::Algebraic Geometry ,0103 physical sciences ,FOS: Mathematics ,Number Theory (math.NT) ,010307 mathematical physics ,Mathematics - Dynamical Systems ,0101 mathematics ,Algebraic number ,Algebraic Geometry (math.AG) ,Mathematics - Abstract
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.
- Published
- 2018