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For a variety $X$ (a toric subvariety, say) over a $p$-adic field $k$, its reduction to a variety $X_p$ over residue field $k_p$ of $k$ and its tropicalization to $X_{tr}$ seem to me to be somewhat orthogonal processes.

Taken individually neither $X_p$ nor $X_{tr}$ suffices to reconstruct $X$ by itself in general. The question is: how far can they go towards reconstruction when taken together? How much flesh can the reduction $X_p$ put on the tropical skeleton $X_{tr}$?

For a variety $X$ over a $p$-adic field $k$, its reduction to a variety $X_p$ over residue field $k_p$ of $k$ and its tropicalization to $X_{tr}$ seem to me to be somewhat orthogonal processes.

Taken individually neither $X_p$ nor $X_{tr}$ suffices to reconstruct $X$ in general. The question is: how far can they go towards reconstruction when taken together?

For a variety $X$ (a toric subvariety, say) over a $p$-adic field $k$, its reduction to a variety $X_p$ over residue field $k_p$ of $k$ and its tropicalization to $X_{tr}$ seem to me to be somewhat orthogonal processes.

Taken individually neither $X_p$ nor $X_{tr}$ suffices to reconstruct $X$ by itself in general. The question is: how far can they go towards reconstruction when taken together? How much flesh can the reduction $X_p$ put on bones of the tropical skeleton $X_{tr}$?

For a variety $X$ (a toric subvariety, say) over a $p$-adic field $k$, its reduction to a variety $X_p$ over residue field $k_p$ of $k$ and its tropicalization to $X_{tr}$ seem to me to be somewhat orthogonal processes.

Taken individually neither $X_p$ nor $X_{tr}$ suffices to reconstruct $X$ by itself in general. The question is: how far can they go towards reconstruction when taken together? How much flesh can the reduction $X_p$ put on the tropical skeleton $X_{tr}$?