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For an abelian variety $A$ of dimension $g$ over a number field $K$, a prime of good reduction (for $A$) is a prime $\mathfrak{p}$ of $K$ for which the reduction of $A$ modulo $\mathfrak{p}$ is an abelian variety of dimension $g$ over the residue field at $\mathfrak{p}$. This holds for all but finitely many primes $\mathfrak{p}$; those for which it does not are primes of bad reduction.

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  • Review status: beta
  • Last edited by Andrew Sutherland on 2016-08-31 00:19:16
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