Arithmetic Moduli of Elliptic Curves

This work is a comprehensive treatment of recent developments in the study of elliptic curves and their moduli spaces. The arithmetic study of the moduli spaces began with Jacobi's "e;Fundamenta Nova"e; in 1829, and the modern theory was erected by Eichler-Shimura, Igusa, and Deligne-Rapoport. In the past decade mathematicians have made further substantial progress in the field. This book gives a complete account of that progress, including not only the work of the authors, but also that of Deligne and Drinfeld.