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For an abelian variety $A$ of dimension $g$ over a number field $K$, a prime of bad reduction (for $A$) is a prime $\mathfrak{p}$ of $K$ for which the reduction of $A$ modulo $\mathfrak{p}$ is not an abelian variety of dimension $g$ over the residue field at $\mathfrak{p}$. The number of primes of bad reduction is always finite; these are precisely the primes that divide the conductor of $A$.

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• Review status: beta
• Last edited by Andrew Sutherland on 2015-08-04 12:01:49
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