Variation of the Faltings height in a \(\overline{\mathbb{Q}}\)-isogeny class of elliptic curves

DOI10.1215/S0012-7094-99-09703-XzbMath0952.11018OpenAlexW2046740849MaRDI QIDQ1974902

Emmanuel Ullmo, Lucien Szpiro

Publication date: 27 March 2000

Published in: Duke Mathematical Journal (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1215/s0012-7094-99-09703-x

zbMATH Keywords

conductorArakelov theoryisogeny classFaltings height

Mathematics Subject Classification ID

Galois theory (11R32) Elliptic curves over global fields (11G05) Heights (11G50) Arithmetic varieties and schemes; Arakelov theory; heights (14G40)

Related Items (5)

Répartition galoisienne ultramétrique d’une classe d’isogénie de courbes elliptiques : Le cas de la mauvaise réduction. Application aux hauteurs locales. ⋮ RÉPARTITION GALOISIENNE D'UNE CLASSE D'ISOGÉNIE DE COURBES ELLIPTIQUES ⋮ Average height of isogenous abelian varieties ⋮ Hyperbolic Galois distribution of an isogeny class of elliptic curves ⋮ The effective Shafarevich conjecture for abelian varieties of -type

Cites Work

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• Calculus on arithmetic surfaces
• Rational isogenies of prime degree. (With an appendix by D. Goldfeld)
• Hecke points on modular curves
• Galois properties of points of finite order of elliptic curves
• INTERSECTION THEORY OF DIVISORS ON AN ARITHMETIC SURFACE
• Points Entiers, Points de Torsion et Amplitude Arithmetique

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