ScalingStacks

Claim 5.2 . [00LX]

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Claim 5.2.

For any i∈{0,…,d}i\in\{0,\dots,d\}, one has

∥Ti∥ϕ=ri=|Ti|ϕ​(x⁡(𝒓)).\lVert T_{i}\rVert_{\phi}=r_{i}=\lvert T_{i}\rvert_{\phi}(x(\boldsymbol{r})).

In other words, the maximum of the function |Ti|ϕ​(x)\lvert T_{i}\rvert_{\phi}(x) on (ℙkd)an(\mathbb{P}^{d}_{k})^{\mathrm{an}} is rir_{i}, and the maximum values of these d+1d+1 functions can be attained at the same point x⁡(𝒓)x(\boldsymbol{r}).

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