ScalingStacks

Definition 2.4 . [03AT]

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Definition 2.4.

Let (𝔙,𝔏)({\mathfrak{V}},{\mathfrak{L}}) be a formal K∘{K^{\circ}}-model of (V,L)(V,L) as in 2.2. Then we get an associated formal metric βˆ₯βˆ₯𝔏{\|\hskip 4.30554pt\|}_{\mathfrak{L}} on LL uniquely determined by requiring β€–s‖𝔏=1\|s\|_{\mathfrak{L}}=1 on the generic fibre WW of any frame ss of 𝔏{\mathfrak{L}} over any formal open subset π”š{\mathfrak{W}} of 𝔙{\mathfrak{V}}. This is well-defined because a change of frame involves an invertible function ff on π”š{\mathfrak{W}} and we have |f|=1|f|=1 on WW.

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