PlanetMath: isogeny

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isogeny

(Definition)

Let and be elliptic curves over a field . An isogeny between and is a finite morphism $f : E\to E'$ of varieties that preserves basepoints.

The two curves are called isogenous if there is an isogeny between them. This is an equivalence relation, symmetry being due to the existence of the dual isogeny. Every isogeny is an algebraic homomorphism and thus induces homomorphisms of the groups of the elliptic curves for -valued points.

"isogeny" is owned by mathcam. [ full author list (2) | owner history (1) ]

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Other names:

isogenous

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Cross-references: points, groups, induces, homomorphism, algebraic, dual isogeny, symmetry, equivalence relation, curves, basepoints, preserves, varieties, finite morphism, field, elliptic curves
There are 5 references to this entry.

This is version 5 of isogeny, born on 2002-07-25, modified 2006-02-17.
Object id is 3206, canonical name is Isogeny.
Accessed 5198 times total.

Classification:

AMS MSC:	14-00 (Algebraic geometry :: General reference works )
	14A10 (Algebraic geometry :: Foundations :: Varieties and morphisms)
	14A15 (Algebraic geometry :: Foundations :: Schemes and morphisms)
	14H52 (Algebraic geometry :: Curves :: Elliptic curves)

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