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In mathematics, a '''Néron differential''', named after [[André Néron]], is an almost canonical choice of [[One-form|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 model]]s.
 
For an elliptic curve of the form
:<math> y^2+a_1xy+a_3=x^3+a_2x^2_2+a_4x+a_6</math>
the Néron differential is
:<math>\frac{dx}{2y+a_1x+a_3}</math>
 
==References==
* {{Citation | last1=Bosch | first1=Siegfried | last2=Lütkebohmert | first2=Werner | last3=Raynaud | first3=Michel | author3-link= Michel Raynaud | title=Néron models | publisher=[[Springer-Verlag]] | location=Berlin, New York | series=[[Ergebnisse der Mathematik und ihrer Grenzgebiete]] (3)| isbn=978-3-540-50587-7 | id={{MathSciNet | id = 1045822}} | year=1990 | volume=21}}
* {{Citation | last1=Néron | first1=André | author1-link= André Néron | title=Modèles minimaux des variétes abèliennes sur les corps locaux et globaux | url=http://www.numdam.org/item?id=PMIHES_1964__21__5_0 | id={{MathSciNet | id = 0179172}} | year=1964 | journal=[[Publications Mathématiques de l'IHÉS]] | volume=21 | pages=5–128 | doi=10.1007/BF02684271}}
 
{{DEFAULTSORT:Neron differential}}
[[Category:Elliptic curves]]
 
 
{{differential-geometry-stub}}

Revision as of 21:35, 5 September 2013

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

y2+a1xy+a3=x3+a2x22+a4x+a6

the Néron differential is

dx2y+a1x+a3

References

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