On the Tate pairing associated to an isogeny between abelian varieties over pseudofinite field

• Date: 2018
• Main Author: Nesteruk, Volodymyr
• Format: Article
• Language: English
• Published: Lugansk National Taras Shevchenko University 2018
• Subjects: pseudofinite field; isogeny; Tate pairing associated to an isogeny; 12G99; 14H05; 14K02
• Online Access: https://admjournal.luguniv.edu.ua/index.php/adm/article/view/759
• Journal Title: Algebra and Discrete Mathematics

In this note, we consider the Tate pairing associated to an isogeny between abelian varieties over pseudofinite field. P. Bruin [1] defined this pairing over finite field \(k\): \(\mathrm{ker}\,\hat{\phi}(k) \; \times \; \mathrm{coker}\,(\phi(k)) \longrightarrow k^*\), and proved its perfectness ove...