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: ker ˆφ(k) × coker(φ(k)) ⟶ k∗, and proved its perfectness over finite field. We prove perfectness of the Tate pairing associate...
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| Veröffentlicht in: | Algebra and Discrete Mathematics |
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| Datum: | 2013 |
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| Format: | Artikel |
| Sprache: | Englisch |
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Інститут прикладної математики і механіки НАН України
2013
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| Online Zugang: | https://nasplib.isofts.kiev.ua/handle/123456789/152312 |
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| Zitieren: | On the Tate pairing associated to an isogeny between abelian varieties over pseudofinite field / V. Nesteruk // Algebra and Discrete Mathematics. — 2013. — Vol. 16, № 1. — С. 103–106. — Бібліогр.: 8 назв. — англ. |
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Digital Library of Periodicals of National Academy of Sciences of Ukraine| _version_ | 1862598255519465472 |
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| author | Nesteruk, V. |
| author_facet | Nesteruk, V. |
| citation_txt | On the Tate pairing associated to an isogeny between abelian varieties over pseudofinite field / V. Nesteruk // Algebra and Discrete Mathematics. — 2013. — Vol. 16, № 1. — С. 103–106. — Бібліогр.: 8 назв. — англ. |
| collection | DSpace DC |
| container_title | Algebra and Discrete Mathematics |
| 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: ker ˆφ(k) × coker(φ(k)) ⟶ 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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| first_indexed | 2025-11-27T18:48:13Z |
| format | Article |
| fulltext | |
| id | nasplib_isofts_kiev_ua-123456789-152312 |
| institution | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| issn | 1726-3255 |
| language | English |
| last_indexed | 2025-11-27T18:48:13Z |
| publishDate | 2013 |
| publisher | Інститут прикладної математики і механіки НАН України |
| record_format | dspace |
| spelling | Nesteruk, V. 2019-06-09T17:19:24Z 2019-06-09T17:19:24Z 2013 On the Tate pairing associated to an isogeny between abelian varieties over pseudofinite field / V. Nesteruk // Algebra and Discrete Mathematics. — 2013. — Vol. 16, № 1. — С. 103–106. — Бібліогр.: 8 назв. — англ. 1726-3255 2010 MSC:12G99, 14H05, 14K02. https://nasplib.isofts.kiev.ua/handle/123456789/152312 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: ker ˆφ(k) × coker(φ(k)) ⟶ 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]. en Інститут прикладної математики і механіки НАН України Algebra and Discrete Mathematics On the Tate pairing associated to an isogeny between abelian varieties over pseudofinite field Article published earlier |
| spellingShingle | On the Tate pairing associated to an isogeny between abelian varieties over pseudofinite field Nesteruk, V. |
| 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 |
| url | https://nasplib.isofts.kiev.ua/handle/123456789/152312 |
| work_keys_str_mv | AT nesterukv onthetatepairingassociatedtoanisogenybetweenabelianvarietiesoverpseudofinitefield |