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  "body": "\n## Summary\n\nLet $R$ be a [[discrete valuation ring|MGM3CNJW9V]] with fraction field $K$.\nThe Néron model of an [[abelian variety|R7W03TXRS9]] over $K$ is its best smooth model over $R$.\nIt is a smooth [[group scheme|TJ04VQP4NB]] of finite type over $R$, characterized by a universal property for maps from smooth $R$-schemes.\nAndré Néron proved that it always exists.\nIts special fibre describes the reduction of the abelian variety, even when the reduction is bad.\n\n## Explanations\n\n### L1 human\n\nAn abelian variety given by equations with rational coefficients can be reduced modulo a prime, but the reduction may become singular.\nOne would like a version over the $p$-adic integers that is as good as possible.\nThe Néron model is that version: it is smooth, and every rational point extends to a point of the model.\nWhen the variety has good reduction, the Néron model is just the abelian scheme given by good equations.\n",
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