Talk:Isogeny

Latest comment: 5 years ago by 2A02:1206:4553:25C0:BD20:90F:2CD3:BFB9 in topic The figure is no good

Definition of "isogeny"

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In its current version, this article defines "isogeny" by "an isogeny is a morphism of varieties between two abelian varieties (e.g. elliptic curves) that is surjective and has a finite kernel". I'm not even sure whether this definition is correct but, anyway, wouldn't it be simpler and clearer to use the standard definition of "isogeny" one can find in standard books on abelian varieties: "A homomorphism f: A -> B of abelian varieties A and B is called an isogeny if f is surjective and has a finite kernel"? See Lang's Abelian Varieties, [II, §1], remark after Theorem 6; Mumford's Abelian Varieties, II.6, Application 3; Milne's Abelian Varieties course notes, text before Proposition 7.1 in chapter I, http://www.jmilne.org/math/ Chrgue (talk) 21:14, 15 December 2010 (UTC)Reply

Some comments:
The definition of "isogeny" thus seems to require a clarification that depends on context.— Pingkudimmi 08:54, 19 July 2018 (UTC)Reply

self isogenies

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What structure do the set of self isogenies have? Do some or all of them have inverses so that those with inverse form a group? If so does the group of invertible selfisogenies transitively map every point on a curve, say, to every other point on the curve or perhaps points that are associated to monic polynomials are mapped just among themselves, analogous to a Galois group mapping roots to roots? (These questions could contribute to expansion of the article, although for my curiousity also. So I'm sure they meet talk page guidelines.) Thanks, Rich Peterson24.7.28.186 (talk) 16:31, 28 October 2011 (UTC)Reply

The figure is no good

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What are omega_1 and omega_2? Where does the lattice come from? — Preceding unsigned comment added by 2A02:1206:4553:25C0:BD20:90F:2CD3:BFB9 (talk) 21:29, 2 July 2019 (UTC)Reply