Output details
10 - Mathematical Sciences
University of Warwick
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Article title
Bornes optimales pour la différence entre la hauteur de Weil et la hauteur de Néron–Tate sur les courbes elliptiques sur Q
Type
D - Journal article
Title of journal
Acta Arithmetica
Article number
-
Volume number
160
Issue number
4
First page of article
385
ISSN of journal
1730-6264
Year of publication
2013
URL
-
Number of additional authors
-
Additional information
-
Interdisciplinary
-
Cross-referral requested
-
Research group
None
Proposed double-weighted
No
Double-weighted statement
-
Reserve for a double-weighted output
No
Non-English
Yes
English abstract
We give an algorithm that, given an elliptic curve $E$ over $\Qbar$ in Weierstrass form, computes the infimum and supremum of the difference between the naïve and canonical height functions on $E(\Qbar)$.
Although this height difference has been studied intensively, previously proven bounds were not sharp; our result is the first to give the upper and lower bounds to any precision. The main ingredient is a careful study of the Archimedean contributions to the height difference function. We give examples comparing our algorithm with
existing methods.
