ScalingStacks

Claim 3.3.1 . [026U]

Original official author HTML, exact retained edition. Historical TeX conversion verdicts remain unchanged. Cited-edition alignment and mathematical self-containment are not assessed.

Complete original source context · Original author HTML

Claim 3.3.1.

For a fixed j∈Ij\in I, if we set e~i=ai​j​e~j\tilde{e}_{i}=a_{ij}\tilde{e}_{j} on UjU_{j} (ai​j∈𝒪Uja_{ij}\in\mathscr{O}_{U_{j}}), then

|e~j|V¯quot​(x)=1maxi=0,…,r⁡{|ai​j|x‖ei‖}|\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 UjanU_{j}^{\mathrm{an}}.

Original mathematics by the credited authors. Source-backed reader collection; mathematical self-containment is not assessed.