The Tate pairing for Abelian varieties over finite fields
Journal de Théorie des Nombres de Bordeaux, Volume 23 (2011) no. 2, pp. 323-328.

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.

Nous décrivons un accouplement arithmétique associé à une isogenie entre variétés abéliennes sur un corps fini. Nous montrons qu’il généralise l’accouplement de Frey et Rück, donnant ainsi une démonstration brève de la perfection de ce dernier.

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DOI: 10.5802/jtnb.764
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     title = {The {Tate} pairing for {Abelian} varieties over finite fields},
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Peter Bruin. The Tate pairing for Abelian varieties over finite fields. Journal de Théorie des Nombres de Bordeaux, Volume 23 (2011) no. 2, pp. 323-328. doi : 10.5802/jtnb.764. https://jtnb.centre-mersenne.org/articles/10.5802/jtnb.764/

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