Suppose $A_0$ is an abelian variety over $\mathbb{C}$, $E$ is a CM field ,denote $A= A_0\otimes_Q E$, is there an isomorphism $ H_1(A_0\otimes_Q E,Q)=H_1(A_0,Q)\otimes_Q E$?how it comes?
homology of abelian variety ?
TOM
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