Linear Tropicalizations

Let X be a closed algebraic subset of 𝔸^n(K) where K is an algebraically closed field complete with respect to a nontrivial non-Archimedean valuation. We show that there is a surjective continuous map from the Berkovich space of X to an inverse limit of a certain family of embeddings of X called linear tropicalizations of X. This map is injective on the subset of the Berkovich space X^an which contains all seminorms arising from closed points of X. We show that the map is a homeomorphism if X is a non-singular algebraic curve. Some applications of these results to transversal intersections are given. In particular we prove that there exists a tropical line arrangement which is realizable by a complex line arrangement but not realizable by any real line arrangement.