ScalingStacks

Proposition 3.8 . [038T]

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Proposition 3.8.

Let 𝒳\mathscr{X} be a strictly semistable model of XX with canonical retraction τ:𝒳→S⁡(𝒳)\tau\colon\mathscr{X}\to S(\mathscr{X}). Let θ∈𝒵1,1​(X)\theta\in\mathcal{Z}^{1,1}(X) be determined on 𝒳\mathscr{X} and let φ:Xan→ℝ\varphi\colon X^{{\mathrm{an}}}\to\mathbb{R} be an arbitrary θ\theta-psh model function. Then φ∘τ:Xan→ℝ\varphi\circ\tau\colon X^{{\mathrm{an}}}\to\mathbb{R} is a θ\theta-psh model function with φ≤φ∘τ\varphi\leq\varphi\circ\tau.

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