ScalingStacks

Proposition 2.23 . [02J4]

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Proposition 2.23.

With the above notation, let p∈Xalganp\in X^{{\text{\rm an}}}_{{\text{\rm alg}}}. Let p~\widetilde{p} as in (2.20). This is a closed algebraic curve. Let ss be a local section of LL defined at pp and such that s⁡(p)≠0s(p)\not=0. Then

log⁡‖s⁡(p)‖log⁡|ϖ|=(p~⋅div⁡(s⊗e))e[ℋ(p):K].\frac{\log\|s(p)\|}{\log|\varpi|}=\frac{(\widetilde{p}\cdot\operatorname{div}(s^{\otimes e}))}{e[\mathscr{H}(p):K]}.

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