Definition 18 [03XJ] Original official author HTML, exact retained edition. Historical TeX conversion verdicts remain unchanged. Cited-edition alignment and mathematical self-containment are not assessed.
Source coverage notes 4 original proof heading/text diagnostics lack independently established complete proof boundaries; diagnostic occurrences may overlap and are not a count of distinct proofs. Complete original source context ยท Original author HTML
Definition 18
A model of X X is a scheme of finite type
๐ณ / ๐ช K {\cal X}/{{\cal O}}_{K} flat and proper over
๐ช K {{\cal O}}_{K} , together with an isomorphism
๐ณ ร S โ p โ e โ c โ ( K ) S โ p โ e โ c โ ( ๐ช K ) โ X {\cal X}\times_{Spec(K)}Spec({{\cal O}}_{K})\simeq X .
Denote the special fiber of ๐ณ {\cal X} by
๐ณ 0 := ๐ณ ร S โ p โ e โ c โ ( K ) S โ p โ e โ c โ ( k ) . {\cal X}^{0}:={\cal X}\times_{Spec(K)}Spec(k)\,\,.