ScalingStacks

Definition 18 [03XJ]

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Definition 18

A model of XX is a scheme of finite type ๐’ณ/๐’ชK{\cal X}/{{\cal O}}_{K} flat and proper over ๐’ชK{{\cal O}}_{K}, together with an isomorphism ๐’ณร—Sโ€‹pโ€‹eโ€‹cโ€‹(K)Sโ€‹pโ€‹eโ€‹cโ€‹(๐’ชK)โ‰ƒX{\cal X}\times_{Spec(K)}Spec({{\cal O}}_{K})\simeq X. Denote the special fiber of ๐’ณ{\cal X} by

๐’ณ0:=๐’ณร—Sโ€‹pโ€‹eโ€‹cโ€‹(K)Sโ€‹pโ€‹eโ€‹cโ€‹(k).{\cal X}^{0}:={\cal X}\times_{Spec(K)}Spec(k)\,\,.

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