Geometric Modular Forms and Elliptic Curves: The Story of a Hong Kong Family

This book provides a comprehensive account of the theory of moduli spaces of elliptic curves (over integer rings) and its application to modular forms.

The construction of Galois representations, which play a fundamental role in Wiles' proof of the Shimura-Taniyama conjecture, is given.

In addition, the book presents an outline of the proof of diverse modularity results of two-dimensional Galois representations (including that of Wiles), as well as some of the author's new results in that direction.Contents:An Algebro-Geometric Tool BoxElliptic CurvesGeometric Modular FormsJacobians and Galois RepresentationsModularity ProblemsReadership: Graduates and researchers in number theory.