Isogeny

In mathematics, particularly in algebraic geometry, an isogeny is a morphism of algebraic groups (also known as group varieties) that is surjective and has a finite kernel.

If the groups are abelian varieties, then any morphism $f : A \to B$ of the underlying algebraic varieties which is surjective with finite fibres is automatically an isogeny, provided that $f (1 A) = 1 B$ . Such an isogeny $f$ then provides a group homomorphism between the groups of $k$ -valued points of $A$ and $B$ , for any field $k$ over which $f$ is defined.

The terms "isogeny" and "isogenous" come from the Greek word ισογενη-ς, meaning "equal in kind or nature". The term "isogeny" was introduced by Weil; before this, the term "isomorphism" was somewhat confusingly used for what is now called an isogeny.

This article is issued from Wikipedia. The text is licensed under Creative Commons - Attribution - Sharealike. Additional terms may apply for the media files.