Given an abelian group scheme $A$, its *dual* $A^\vee$ is essentially the moduli space of line bundles over $A$, the Picard scheme of $A$. Accordingly, there is a canonical line bundle over the product $A \times A^\vee$ (which over each point $(a,P)$ is the fiber over $a$ of the line bundle $P$): the *Poincaré line bundle*.

A standard textbook is

- Mumford,
*Abelian varieties*

A review of some basics is in

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