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A variety $X$ over a number field $K$ is said to have good reduction at a prime $\mathfrak{p}$ if it has a model over $\mathcal{O}_{K, \mathfrak{p}}$ whose reduction modulo $\mathfrak{p}$ defines a smooth variety of the same dimension; otherwise, $\mathfrak{p}$ 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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  • Review status: beta
  • Last edited by Raymond van Bommel on 2020-08-25 08:09:47
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