ScalingStacks

Theorem A. [04M5]

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Theorem A.

There exists a continuous retraction π:Xan→Sk⁡(X)\pi:X^{\an}\rightarrow\Sk(X) such that

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    π\pi can be written as a composition π′∘ρ𝒳′\pi^{\prime}\circ\rho_{\mathscr{X}^{\prime}}, with 𝒳′\mathscr{X}^{\prime} being an snc model of XX and π′:Sk⁡(𝒳′)→Sk⁡(X)\pi^{\prime}:\Sk(\mathscr{X}^{\prime})\rightarrow\Sk(X) a piecewise-linear map;

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    π\pi is an affinoid torus fibration outside a piecewise-linear locus Γ\Gamma, that has codimension 22 and is contained in the 22-skeleton of Sk⁡(X)\Sk(X);

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    π\pi induces an integral affine structure on Sk⁡(X)∖Γ\Sk(X)\setminus\Gamma, which is isomorphic to the ones constructed in [Gro01], [Gro05], and [Rua01].

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