This extremely terse definition needs some further explanation.
The group law on an abelian variety is commutative.
This implies that for every ring , the -points of an abelian variety form an abelian group.
An abelian variety is projective.
If is a curve, then the Jacobian of is an abelian variety. This example motivated the development of the theory of abelian varieties, and many properties of curves are best understood by looking at the Jacobian.
See Mumford’s excellent book Abelian Varieties. The bibliography for algebraic geometry has details and other books.
|Date of creation||2013-03-22 14:17:17|
|Last modified on||2013-03-22 14:17:17|
|Last modified by||archibal (4430)|