Claim 3.3.1 . [026U]

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Claim 3.3.1.

For a fixed $j\in I$ , if we set $\tilde{e}_{i}=a_{ij}\tilde{e}_{j}$ on $U_{j}$ ( $a_{ij}\in\mathscr{O}_{U_{j}}$ ), then

|\tilde{e}_{j}|_{\overline{V}}^{\mathrm{quot}}(x)=\frac{1}{\displaystyle{\max_{i=0,\ldots,r}\left\{\frac{|a_{ij}|_{x}}{\|e_{i}\|}\right\}}}

on $U_{j}^{\mathrm{an}}$ .