ScalingStacks

Lemma 5.39 . [02U3]

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Lemma 5.39.

Let Π\Pi be a complete SCR polyhedral complex of NℝN_{\mathbb{R}} such that rec⁡(Π)=Σ\operatorname{rec}(\Pi)=\Sigma. Let 𝒳:=𝒳Π{\mathcal{X}}:={\mathcal{X}}_{\Pi} be the model of XΣX_{\Sigma} determined by Π\Pi. Let Λ∈Π\Lambda\in\Pi and p∈X0anp\in X_{0}^{{\text{\rm an}}}. Then red⁡(p)∈𝒳Λ{\operatorname{red}}(p)\in{\mathcal{X}}_{\Lambda} if and only if valK⁡(p)∈Λ{\operatorname{val}}_{K}(p)\in\Lambda.

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