About the Teyt-Shafarevich product in elliptical curves over pseudolocal fields with remainder fields of the characteristics 3
Let$k$  be a general local field with pseudolocal residue field $\kappa$, ${\rm char} \kappa = 3$, and $А$  an elliptic curve defined over $k$. It is proved that the Tate-Shafarevich product $H^1(k, A) \times A_k→ Q/ \mathbb Z$  of the group $H^1 (k, А)$ of pri...
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| Datum: | 1992 |
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| Hauptverfasser: | , |
| Format: | Artikel |
| Sprache: | Ukrainisch |
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Institute of Mathematics, NAS of Ukraine
1992
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| Online Zugang: | https://umj.imath.kiev.ua/index.php/umj/article/view/8163 |
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| Назва журналу: | Ukrains’kyi Matematychnyi Zhurnal |
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Ukrains’kyi Matematychnyi Zhurnal| _version_ | 1860512944405610496 |
|---|---|
| author | Andriichuk , V. I. Андрійчук , В. І. |
| author_facet | Andriichuk , V. I. Андрійчук , В. І. |
| author_sort | Andriichuk , V. I. |
| baseUrl_str | https://umj.imath.kiev.ua/index.php/umj/oai |
| collection | OJS |
| datestamp_date | 2024-02-26T13:58:10Z |
| description | Let$k$  be a general local field with pseudolocal residue field $\kappa$, ${\rm char} \kappa = 3$, and $А$  an elliptic curve defined over $k$. It is proved that the Tate-Shafarevich product $H^1(k, A) \times A_k→ Q/ \mathbb Z$  of the group $H^1 (k, А)$ of principal homogeneous spaces of the curve $А$ over $ k$ and the group $А_к$  of its $k$-rational points is left nondegenerate. |
| first_indexed | 2026-03-24T03:36:50Z |
| format | Article |
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| id | umjimathkievua-article-8163 |
| institution | Ukrains’kyi Matematychnyi Zhurnal |
| keywords_txt_mv | keywords |
| language | Ukrainian |
| last_indexed | 2026-03-24T03:36:50Z |
| publishDate | 1992 |
| publisher | Institute of Mathematics, NAS of Ukraine |
| record_format | ojs |
| resource_txt_mv | umjimathkievua/26/259e232f656a896f0ecea3f255f48c26.pdf |
| spelling | umjimathkievua-article-81632024-02-26T13:58:10Z About the Teyt-Shafarevich product in elliptical curves over pseudolocal fields with remainder fields of the characteristics 3 Про добуток Тейта—Шафаревича в еліптичних кривих над псевдолокальними полями з полями лишків характеристики 3 Andriichuk , V. I. Андрійчук , В. І. - Let$k$  be a general local field with pseudolocal residue field $\kappa$, ${\rm char} \kappa = 3$, and $А$  an elliptic curve defined over $k$. It is proved that the Tate-Shafarevich product $H^1(k, A) \times A_k→ Q/ \mathbb Z$  of the group $H^1 (k, А)$ of principal homogeneous spaces of the curve $А$ over $ k$ and the group $А_к$  of its $k$-rational points is left nondegenerate. Пусть $k$  — общее локальное поле с псевдоконечным полем вычетов $\kappa$, ${\rm char} \kappa = 3$, $А$  — эллиптическая кривая, определенная над полем $k$. Доказано, что произведение Тэйта — Шафаревича $H^1(k, A) \times A_k → Q/ \mathbb Z$ группы $H^1 (k, А)$  — главных однородных пространств кривой $А$  над полем $k$  — и группы $А_к$  ее $k$-рациональных точек невырождено слева. Нехай $k$ — загальне локальне поле з псевдоскінченним полем лишків $\kappa$, ${\rm char} \kappa = 3$, $А$ — еліптична крива, визначена над полем $k$. Доведено, що добуток Тейта — Шафаревича $H^1(k, A) \times A_k → Q/ \mathbb Z$ групи $H^1 (k, А)$ —головних однорідних просторів кривої $А$ над полем $k$ — і групи $А_к$ її $k$-раціональних точок невироджений зліва. Institute of Mathematics, NAS of Ukraine 1992-10-07 Article Article application/pdf https://umj.imath.kiev.ua/index.php/umj/article/view/8163 Ukrains’kyi Matematychnyi Zhurnal; Vol. 44 No. 9 (1992); 1157-1165 Український математичний журнал; Том 44 № 9 (1992); 1157-1165 1027-3190 uk https://umj.imath.kiev.ua/index.php/umj/article/view/8163/9687 Copyright (c) 1992 V. I. Andriichuk |
| spellingShingle | Andriichuk , V. I. Андрійчук , В. І. About the Teyt-Shafarevich product in elliptical curves over pseudolocal fields with remainder fields of the characteristics 3 |
| title | About the Teyt-Shafarevich product in elliptical curves over pseudolocal fields with remainder fields of the characteristics 3 |
| title_alt | Про добуток Тейта—Шафаревича в еліптичних кривих над псевдолокальними полями з полями лишків характеристики 3 |
| title_full | About the Teyt-Shafarevich product in elliptical curves over pseudolocal fields with remainder fields of the characteristics 3 |
| title_fullStr | About the Teyt-Shafarevich product in elliptical curves over pseudolocal fields with remainder fields of the characteristics 3 |
| title_full_unstemmed | About the Teyt-Shafarevich product in elliptical curves over pseudolocal fields with remainder fields of the characteristics 3 |
| title_short | About the Teyt-Shafarevich product in elliptical curves over pseudolocal fields with remainder fields of the characteristics 3 |
| title_sort | about the teyt-shafarevich product in elliptical curves over pseudolocal fields with remainder fields of the characteristics 3 |
| topic_facet | - |
| url | https://umj.imath.kiev.ua/index.php/umj/article/view/8163 |
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