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Isogenyとは 意味・読み方・使い方
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意味・対訳 数学で、同種写像(isogeny)とは、2つのアーベル多様体(例えば楕円曲線)の間の代数群の射で、全射でしかも有限の核を持っているものを言う。
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Wiktionary英語版での「Isogeny」の意味 |
isogeny
名詞
isogeny (countable かつ uncountable, 複数形 isogenies)
- The condition of being isogenous.
- (algebraic geometry, category theory) An epimorphism of group schemes that is surjective and has a finite kernel.
- 2000, Marc Hindry, Joseph H. Silverman, Diophantine Geometry: An Introduction, Springer, page 95,
- It is clear that if is connected, then two of the defining properties of an isogeny imply the third.
- 2002, Mireille Fouquet, François Morain, Isogeny Volcanoes and the SEA Algorithm, Claus Fieker, David R. Kohel (editors), Algorithmic Number Theory: 5th International Symposium, Proceedings, Springer, LNCS 2369, page 279,
- 2005, Fred Diamond, Jerry Shurman, A First Course in Modular Forms, Springer, page 29,
- The dual isogeny of an isomorphism is its inverse. The dual of a composition of isogenies is the composition of the duals in the reverse order. If is an isogeny and is its dual then the formulas , show that also
- ,
- so that is in turn the dual isogeny of its dual . Isogeny of complex tori, rather than isomorphism, will turn out to be the appropriate equivalence relation in the context of modular forms.
- The dual isogeny of an isomorphism is its inverse. The dual of a composition of isogenies is the composition of the duals in the reverse order. If is an isogeny and is its dual then the formulas , show that also
- 2000, Marc Hindry, Joseph H. Silverman, Diophantine Geometry: An Introduction, Springer, page 95,
使用する際の注意点
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 Epimorphism on Wikipedia.)
Further reading
- Isogeny on Encyclopedia of Mathematics
- Isogeny on Wolfram MathWorld
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