Explore: Abelian Varieties

i.e., has a group law that can be defined by regular functions. Abelian varieties are at the same time among the most studied objects in algebraic geometry

mathematics, the arithmetic of abelian varieties is the study of the number theory of an abelian variety, or a family of abelian varieties. It goes back to the

involution), leading to a classification of CM-type abelian varieties. To construct such varieties in the same style as for elliptic curves, starting with

In algebraic geometry, a semistable abelian variety is an abelian variety defined over a global or local field, which is characterized by how it reduces

an abelian variety A to another one B is a surjective morphism with finite kernel. Some theorems on abelian varieties require the idea of abelian variety

conjecture holds for sufficiently general abelian varieties, for products of elliptic curves, and for simple abelian varieties of prime dimension. However, Mumford

Abelian varieties are a natural generalization of elliptic curves to higher dimensions. However, unlike the case of elliptic curves, there is no well-behaved

higher-dimensional abelian varieties, so the concept of dual becomes more interesting in higher dimensions. Let A be an abelian variety over a field k. We

algebraic groups (also known as group varieties) that is surjective and has a finite kernel. If the groups are abelian varieties, then any morphism f : A → B of

Another class is formed by the abelian varieties, which are the algebraic groups whose underlying variety is a projective variety. Chevalley's structure theorem