Definitions For Isogeny

Noun

ISOGENY (plural isogenies) The condition of being isogenous. (algebraic geometry, category theory) An epimorphism of group schemes that is surjective and has a finite kernel.

Usage notes

In some contexts, (e.g., universal algebra), an epimorphism may be defined as a surjective homomorphism, and the definition of isogeny may change accordingly. In the broader context of category theory, however, this substitution is not made, because the definitions are not precisely identical. (A surjective homomorphism is always an epimorphism, but the reverse is not always true. See {{pedialite, Epimorphism}})

Derived terms

dual isogeny isogenic isogenous isogeny cycle isogeny graph isogeny volcano

Translations

Finnish: isogenia

Etymology

{{confix, en, iso, geny}}.