A variety $X$ over $\mathbb{Q}$ is said to have **good reduction** at a prime $p$ if it has an integral model whose reduction modulo $p$ defines a smooth variety of the same dimension; otherwise, $p$ is said to be a prime of **bad reduction**.

When $X$ is a curve, any prime of good reduction for $X$ is also a prime of good reduction for its Jacobian, but the converse need not hold when $X$ has genus $g>1$.

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- Last edited by John Cremona on 2018-05-24 16:48:18

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- 2018-05-24 16:48:18 by John Cremona (Reviewed)