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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| Date: | 2018 |
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| Format: | Article |
| Language: | English |
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Lugansk National Taras Shevchenko University
2018
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| Online Access: | https://admjournal.luguniv.edu.ua/index.php/adm/article/view/759 |
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| Journal Title: | Algebra and Discrete Mathematics |
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Algebra and Discrete Mathematics| _version_ | 1856543268876058624 |
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| author | Nesteruk, Volodymyr |
| author_facet | Nesteruk, Volodymyr |
| author_sort | Nesteruk, Volodymyr |
| baseUrl_str | |
| collection | OJS |
| datestamp_date | 2018-04-26T01:26:05Z |
| description | 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]. |
| first_indexed | 2025-12-02T15:32:30Z |
| format | Article |
| id | admjournalluguniveduua-article-759 |
| institution | Algebra and Discrete Mathematics |
| language | English |
| last_indexed | 2025-12-02T15:32:30Z |
| publishDate | 2018 |
| publisher | Lugansk National Taras Shevchenko University |
| record_format | ojs |
| spelling | admjournalluguniveduua-article-7592018-04-26T01:26:05Z On the Tate pairing associated to an isogeny between abelian varieties over pseudofinite field Nesteruk, Volodymyr pseudofinite field, isogeny, Tate pairing associated to an isogeny 12G99, 14H05, 14K02 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]. Lugansk National Taras Shevchenko University 2018-04-26 Article Article Peer-reviewed Article application/pdf https://admjournal.luguniv.edu.ua/index.php/adm/article/view/759 Algebra and Discrete Mathematics; Vol 16, No 1 (2013) 2415-721X 1726-3255 en https://admjournal.luguniv.edu.ua/index.php/adm/article/view/759/288 Copyright (c) 2018 Algebra and Discrete Mathematics |
| spellingShingle | pseudofinite field isogeny Tate pairing associated to an isogeny 12G99 14H05 14K02 Nesteruk, Volodymyr On the Tate pairing associated to an isogeny between abelian varieties over pseudofinite field |
| title | On the Tate pairing associated to an isogeny between abelian varieties over pseudofinite field |
| title_full | On the Tate pairing associated to an isogeny between abelian varieties over pseudofinite field |
| title_fullStr | On the Tate pairing associated to an isogeny between abelian varieties over pseudofinite field |
| title_full_unstemmed | On the Tate pairing associated to an isogeny between abelian varieties over pseudofinite field |
| title_short | On the Tate pairing associated to an isogeny between abelian varieties over pseudofinite field |
| title_sort | on the tate pairing associated to an isogeny between abelian varieties over pseudofinite field |
| topic | pseudofinite field isogeny Tate pairing associated to an isogeny 12G99 14H05 14K02 |
| topic_facet | pseudofinite field isogeny Tate pairing associated to an isogeny 12G99 14H05 14K02 |
| url | https://admjournal.luguniv.edu.ua/index.php/adm/article/view/759 |
| work_keys_str_mv | AT nesterukvolodymyr onthetatepairingassociatedtoanisogenybetweenabelianvarietiesoverpseudofinitefield |