nLab
dual abelian group scheme

Contents

Idea

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

References

A standard textbook is

  • Mumford, Abelian varieties

A review of some basics is in

Last revised on July 4, 2014 at 03:01:02. See the history of this page for a list of all contributions to it.