nLab dual abelian group scheme

Idea

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.

Related concepts

• Picard scheme

• Cartier duality

References

A standard textbook is

• Mumford, Abelian varieties

A review of some basics is in

• Akhil Mathew, Duality for abelian varieties