| 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. |
