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Bornes optimales pour la différence entre la hauteur de Weil et la hauteur de Néron-Tate sur les courbes elliptiques sur ℚ̅

Peter Bruin — 2013

Acta Arithmetica

We give an algorithm that, for an elliptic curve E over ℚ̅ in Weierstraß form, computes the infimum and supremum of the difference between the naïve and canonical height functions on E(ℚ̅).

The Tate pairing for Abelian varieties over finite fields

Peter Bruin — 2011

Journal de Théorie des Nombres de Bordeaux

In this expository note, we describe an arithmetic pairing associated to an isogeny between Abelian varieties over a finite field. We show that it generalises the Frey–Rück pairing, thereby giving a short proof of the perfectness of the latter.

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