Hi, everyone.

I am looking for some references for period matrix of abelian variety over arbitrary field, if you know, could you please tell me?

For period matrix of abelian varieties, I means that if $A$ is an abelian variety over complex number field, $A \cong V/\Gamma$. If we chose a basis of $V$, and a basis of lattice $\Gamma$, write the basis of lattice in term by the basis of $V$, the matrix which is called period matrix.

I want to know how to define period matrix for abelian variety over arbitrary field, and some basic properties of this matrix.

Thank you very much!