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

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.

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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DOI : https://doi.org/10.5802/jtnb.764
@article{JTNB_2011__23_2_323_0,
     author = {Peter Bruin},
     title = {The {Tate} pairing for {Abelian} varieties over finite fields},
     journal = {Journal de Th\'eorie des Nombres de Bordeaux},
     pages = {323--328},
     publisher = {Soci\'et\'e Arithm\'etique de Bordeaux},
     volume = {23},
     number = {2},
     year = {2011},
     doi = {10.5802/jtnb.764},
     mrnumber = {2817932},
     zbl = {1246.11123},
     language = {en},
     url = {https://jtnb.centre-mersenne.org/articles/10.5802/jtnb.764/}
}
Peter Bruin. The Tate pairing for Abelian varieties over finite fields. Journal de Théorie des Nombres de Bordeaux, Tome 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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