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For an abelian variety $A$ over $\Q$, the local factor that appears in the Euler product of its L-function at a bad prime $p$ depends on the type of reduction $A$ has at $p$. In general, the degree of the Euler factor at a bad prime will be less than the degree of the L-function (which is $2g$, where $g$ is the dimension of the abelian variety).

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  • Last edited by John Cremona on 2018-05-23 16:41:18
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