Inégalité du discriminant pour les pinceaux elliptiques à réductions quelconques |
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Authors: | J Pesenti L Szpiro |
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Institution: | (1) Département de Mathématiques, Université de Paris-Sud, Batiment 425, 91405 Orsay, Cedex, France |
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Abstract: | In this article the degree of the discriminant of an elliptic pencil on a projective curve is upper-bounded by using the degree of its conductor and the genus of the base curve. This is done in the most general case, extending a method and a result of Szpiro (1981 and 1990a) and a result of Hindry and Silvermann. The difficult part, dealing with characteristic 2 and 3 and additive reductions, need the introduction of a new object - which we called 'conducteur efficace' - defined by using differentials and interestingly comparable to the usual conductor. This article ends with a few results in the arithmetical case - case corresponding to an inequality conjectured by the second author in 1978: (1) the proof of this inequality in the potentially good reduction cases; (2) the passage from the semi-stable reduction to the general case for a strong inequality. |
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Keywords: | elliptic curves conductors discriminant |
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