A note on tropicalization in the context of Berkovich spaces

Zusammenfassung

Let K be a non-Archimedean non-trivially valued field, and I" be its value group. Let X be a compact strictly K-analytic space and f: X -> be a morphism of K-analytic spaces. We prove that |f|(X) a (c) (a"e*(+)) (n) is a I"-rational polyhedral set whose dimension is less than or equal to dim(X). The main ingredient of the proof is a quantifier elimination theorem for subanalytic sets due to Leonard Lipshitz.