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For an abelian variety $A$ over $\Q$, the local factor that appears in the Euler product of its L-function $L(A,s)$ at a good prime $p$ is an integer polynomial $L_p(T)$ of degree $2p$ that is reciprocal to the characteristic polynomial $\chi(T)$ of the Frobenius endomorphism of the reduction of $A$ modulo $p$, meaning that $L_p(T)=T^{2g}\chi(T^{-1})$.

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  • Review status: reviewed
  • Last edited by Bjorn Poonen on 2022-03-24 17:11:55
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