isogeny
Sign in to saveIn 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.
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Encyclopedic overview
5 sectionsContents
- Degree of isogeny
- Case of abelian varieties
- See also
- References
- External links
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 of the underlying algebraic varieties which is surjective with finite fibres is automatically an isogeny, provided that . Such an isogeny then provides a group homomorphism between the groups of -valued points of and , for any field over which is defined.
Excerpted from Wikipedia’s “isogeny” article, available under the CC BY-SA 4.0 licence.