Néron differential
From HandWiki
In mathematics, a Néron differential, named after André Néron, is an almost canonical choice of 1-form on an elliptic curve or abelian variety defined over a local field or global field. The Néron differential behaves well on the Néron minimal models. For an elliptic curve of the form
- [math]\displaystyle{ y^2+a_1xy+a_3y=x^3+a_2x^2+a_4x+a_6 }[/math]
the Néron differential is
- [math]\displaystyle{ \frac{dx}{2y+a_1x+a_3} }[/math]
References
- Bosch, Siegfried; Lütkebohmert, Werner; Raynaud, Michel (1990), Néron models, Ergebnisse der Mathematik und ihrer Grenzgebiete (3), 21, Berlin, New York: Springer-Verlag, ISBN 978-3-540-50587-7
- Néron, André (1964), "Modèles minimaux des variétés abéliennes sur les corps locaux et globaux", Publications Mathématiques de l'IHÉS 21: 5–128, doi:10.1007/BF02684271, http://www.numdam.org/item?id=PMIHES_1964__21__5_0
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