| Equipe(s) : | tn, |
| Responsables : | Ziyang Gao, Marc Hindry, Bruno Kahn, João Pedro P. dos Santos |
| Email des responsables : | ziyang.gao@imj-prg.fr |
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| Description | http://www.imj-prg.fr/tn/STN/stnj.html
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| Orateur(s) | A. Agashe - , |
| Titre | The Birch and Swinnerton-Dyer conjecture and visibility |
| Date | 14/06/2004 |
| Horaire | 14:00 à 16:00 |
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| Résume | The second part of the Birch and Swinnerton-Dyerconjecture relates the special L-value of an abelianvariety to certain arithmetic invariants of the abelianvariety, including the order of its Shafarevich-Tate group.The theory of visibility, initiated by Mazur, can sometimesbe used to prove the existence of non-trivial elementsof the Shafarevich-Tate group. We will discuss howvisibility can be used to show that a certain factorof the special L-value (assumed non-zero) divides the orderof the Shafarevich-Tate group, under certain hypotheses,the most serious of which is the first part of theBirch and Swinnerton-Dyer conjecture on the rank. |
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