Chambert-Loir and Ducros have introduced real differential forms and currents on Berkovich spaces.(See Gubler's survey for example). In that survey, a tropical chart $V$ is defined on an analytification $X^{\mathrm{an}}$, something like $ \mathrm{val}^{-1}(\Delta)$ for a polyhedron $\Delta$. Here $\mathrm{val}: (K^\times)^n \to \mathbb R^n$ is defined by $(z_1,\dots,z_n) \mapsto (\mathrm{val}(z_1),\dots,\mathrm{val}(z_n))$

**Question:**

I am an beginner for this subject, I don't understand the reason to use tropical charts, what's the advantage? It seems not so good because they are contained in a torus $(K^\times)^n$ so they exclude zero. But in differential geometry local models are $\mathbb R^n$ which include zero.

Let's consider the rigid analytification $$\mathbb A_K^{n,rig} = \cup_{i=0}^\infty \mathrm{Sp} K \langle c^{-i}\zeta_1, \dots, c^{-i}\zeta_n\rangle $$ of the affine $n$-space $\mathbb A^n_K=\mathrm{Spec} K[\zeta_1,\dots,\zeta_n]$ (here $|c|>1$). In this case can we find some good tropical charts?

Other than the example in the question 2 above, can we explicitly give any other tropical charts? say on the Berkovich projective line?

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