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Heights, algebraic dynamics and Berkovich analytic spaces. (English) Zbl 1243.14023
Summary: This paper is an exposition on heights and their importance in the modern study of algebraic dynamics. We explain the idea of canonical height and its surprising relation to algebraic dynamics, invariant measures, arithmetic intersection theory, equidistribution and \(p\)-adic analytic geometry.
MSC:
14G40 Arithmetic varieties and schemes; Arakelov theory; heights
11G50 Heights
14G22 Rigid analytic geometry
37P50 Dynamical systems on Berkovich spaces
37P30 Height functions; Green functions; invariant measures in arithmetic and non-Archimedean dynamical systems
14G20 Local ground fields in algebraic geometry
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