Séminaires : Séminaire Théorie des Nombres

Equipe(s) : tn,
Responsables :Ziyang Gao, Marc Hindry, Bruno Kahn, João Pedro P. dos Santos
Email des responsables : ziyang.gao@imj-prg.fr
Salle :
Adresse :



Orateur(s) A. Agashe - ,
Titre The Birch and Swinnerton-Dyer conjecture and visibility
Horaire14:00 à 16:00
RésumeThe 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.