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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- Last edited by John Cremona on 2018-05-24 16:19:47

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- 2018-05-24 16:19:47 by John Cremona (Reviewed)