An **isogeny** of abelian varieties is a surjective morphism with finite kernel; it is a morphism of algebraic varieties (of the same dimension) and a group homomorphism (with finite kernel).

Two abelian varieties are **isogenous** if there is an isogeny between them. This defines an equivalence relation which determines the set of isogeny classes of abelian varieties.

**Authors:**

**Knowl status:**

- Review status: reviewed
- Last edited by Andrew Sutherland on 2019-04-30 00:02:58

**Referred to by:**

- ag.selmer_group
- av.fq.curve_point_counts
- av.fq.one_rational_point
- av.isogeny_class
- av.polarization
- curve.highergenus.aut.groupalgebradecomp
- ec.isogeny
- g2c.decomposition
- g2c.end_alg
- g2c.geom_end_alg
- g2c.isogeny_class
- modcurve.decomposition
- modcurve.gassmann_class
- lmfdb/genus2_curves/templates/g2c_isogeny_class.html (line 103)

**History:**(expand/hide all)

- 2022-03-26 16:05:25 by Bjorn Poonen
- 2019-04-30 00:02:58 by Andrew Sutherland (Reviewed)
- 2019-04-29 20:02:58 by Andrew Sutherland
- 2015-08-02 22:47:13 by Andrew Sutherland

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