ScalingStacks

Theorem 7.3 (Berkovich, Ducros) [037E]

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Theorem 7.3 (Berkovich, Ducros)

If ZZ is a compact analytic space over KK of dimension nn and if φ:Z→Tan\varphi:Z\rightarrow{T^{\rm an}} is an analytic moment map, then φtrop​(Z){\varphi_{\rm trop}}(Z) is a finite union of integral Γ\Gamma-affine polytopes of dimension at most nn. Moreover, φtrop​(∂Z){\varphi_{\rm trop}}(\partial Z) is contained in a finite union of integral Γ\Gamma-affine polytopes of dimension ≤n−1\leq n-1. If ZZ is affinoid, then φtrop​(∂Z){\varphi_{\rm trop}}(\partial Z) is equal to a finite union of such polytopes.

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