CYCLOTOMIC FIELDS AND MODULAR CURVES

Abstract

The first chapter of this article contains an exposition of the work of Iwasawa and Mazur on the arithmetic of Abelian varieties over cyclotomic fields. The study of questions arising here leads us in the second chapter to the use of the zeta-function apparatus, and the conjectures of Weil and Birch - Swinnerton-Dyer; this permits us to obtain conditional formulae for the order of the Tate-Shafarevich group.