Local L-factors at good primes (reviewed)

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 $L_p(T)=T^{2g}\chi(T^{-1})$.