On the Tate pairing associated to an isogeny between abelian varieties over pseudofinite field
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...
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| Datum: | 2018 |
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| 1. Verfasser: | |
| Format: | Artikel |
| Sprache: | English |
| Veröffentlicht: |
Lugansk National Taras Shevchenko University
2018
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| Online Zugang: | https://admjournal.luguniv.edu.ua/index.php/adm/article/view/759 |
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| Назва журналу: | Algebra and Discrete Mathematics |
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Algebra and Discrete Mathematics| Zusammenfassung: | 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 over finite field. We prove perfectness of the Tate pairing associated to an isogeny between abelian varieties over pseudofinite field, with help of the method, used by P. Bruin in the case of finite ground field [1]. |
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