Lemma 5.57 . [02UY]

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Lemma 5.57.

Let $p\in X_{\Sigma}^{{\text{\rm an}}}$ . Then

{\operatorname{red}}(p)=\begin{cases}q_{0},&\text{ if }|t(p)|<|\varpi|^{a}\\ q_{i},\ i=1\dots,k,&\text{ if }|\varpi|^{a-i+1}<|t(p)|<|\varpi|^{a-i}\\ q_{k+1},&\text{ if }|\varpi|^{a-k}<|t(p)|\\ \eta_{i},\ i=0\dots,k,&\text{ if }|t(p)|=|\varpi|^{a-i}\text{ and }p\in\operatorname{im}(\theta_{\Sigma}).\end{cases}