Néron differential

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

${\displaystyle y^{2}+a_{1}xy+a_{3}=x^{3}+a_{2}x^{2}+a_{4}x+a_{6}}$

the Néron differential is

${\frac {dx}{2y+a_{1}x+a_{3}}}$

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, MR 1045822
• Néron, André (1964), "Modèles minimaux des variétes abèliennes sur les corps locaux et globaux", Publications Mathématiques de l'IHÉS, 21: 5–128, doi:10.1007/BF02684271, MR 0179172