Let $A$ be an abelian variety.(Complex manifold with $A$'s covering admitting a non-degenerate hermitian form on the lattice.) $D_1,D_2$ are 2 algebraically equivalent divisor on abelian variety $A$ if $D_1$ and $D_2$ has the same riemann form. (Any positive divisor can be associated to a $\theta$ function with the given lattice and this $\theta$ function defines a unique anti-symmetric $R-$bilinear form. Then this map can be extended linearly from space of divisor of $A$ as abelian group to space of anti-symmetric riemann forms associated to the lattice.)
$\textbf{Q:}$ Where is this algebraic equivalent divisor definition coming from?(What is correspondence in algebraic geometric setting?) The book says this definition is abstraction of some definition in algebraic geometry but it is not clear. Is this numerical equivalent in neron-severi group? If so, how do I see they are talking about the same definition?
Ref: Sec 8. Analytic Theory of Abelian Varties by Swinnerton-Dyer