Lemma 5.0.3. [04QI]

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Lemma 5.0.3.

Let $\mathscr{X}$ be an snc model of $X$ and assume that $\mathscr{X}$ admits a dominating projective snc model. Then for any stratum $Y$ of $\mathscr{X}_{0}$ , the retraction $\rho_{\mathscr{X}}$ over $\Star(\tau_{Y})$ only depends on the formal completion $\widehat{\mathscr{X}_{/Y}}$ .