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.
@article{JTNB_2011__23_2_323_0,
author = {Bruin, Peter},
title = {The {Tate} pairing for {Abelian} varieties over finite fields},
journal = {Journal de th\'eorie des nombres de Bordeaux},
pages = {323--328},
year = {2011},
publisher = {Soci\'et\'e Arithm\'etique de Bordeaux},
volume = {23},
number = {2},
doi = {10.5802/jtnb.764},
zbl = {1246.11123},
mrnumber = {2817932},
language = {en},
url = {https://www.numdam.org/articles/10.5802/jtnb.764/}
}
TY - JOUR AU - Bruin, Peter TI - The Tate pairing for Abelian varieties over finite fields JO - Journal de théorie des nombres de Bordeaux PY - 2011 SP - 323 EP - 328 VL - 23 IS - 2 PB - Société Arithmétique de Bordeaux UR - https://www.numdam.org/articles/10.5802/jtnb.764/ DO - 10.5802/jtnb.764 LA - en ID - JTNB_2011__23_2_323_0 ER -
%0 Journal Article %A Bruin, Peter %T The Tate pairing for Abelian varieties over finite fields %J Journal de théorie des nombres de Bordeaux %D 2011 %P 323-328 %V 23 %N 2 %I Société Arithmétique de Bordeaux %U https://www.numdam.org/articles/10.5802/jtnb.764/ %R 10.5802/jtnb.764 %G en %F JTNB_2011__23_2_323_0
Bruin, Peter. 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
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