The Néron Model
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Let R bea discrete valuation ring with maximal ideal p and fraction field K, and let E/K be an elliptic curve given by a Weierstrass equation say with coefficients a1, a2, a3, a4, a6 ∈ R. This equation can be used to define a closed subscheme . An elementary property of closed subschemes of projective space says that every point of E(K) extends to give a point of W(R), that is, a section Spec(R) → W.
KeywordsElliptic Curve Group Scheme Residue Field Generic Fiber Discrete Valuation Ring
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