Arithmetic Theory of Elliptic Curves [electronic resource] : Lectures given at the 3rd Session of the Centro Internazionale Matematico Estivo (C.I.M.E.) held in Cetraro, Italy, July 12–19, 1997 / by John H. Coates, Kenneth A. Ribet, Ralph Greenberg, Karl Rubin ; edited by Carlo Viola.

Fragments of the GL2 Iwasawa theory of elliptic curves without complex multiplication -- Iwasawa theory for elliptic curves -- Torsion points on J 0(N) and Galois representations -- Elliptic curves with complex multiplication and the conjecture of Birch and Swinnerton-Dyer.

This volume contains the expanded versions of the lectures given by the authors at the C.I.M.E. instructional conference held in Cetraro, Italy, from July 12 to 19, 1997. The papers collected here are broad surveys of the current research in the arithmetic of elliptic curves, and also contain several new results which cannot be found elsewhere in the literature. Owing to clarity and elegance of exposition, and to the background material explicitly included in the text or quoted in the references, the volume is well suited to research students as well as to senior mathematicians.