Bridging the gap between novice and expert, the aim of this book is to present in a self-contained way a number of striking examples of current diophantine prob

This is an introduction to diophantine geometry at the advanced graduate level. The book contains a proof of the Mordell conjecture which will make it quite att

The purpose of this book is to build the fundament of an Arakelov theory over adelic curves in order to provide a unified framework for research on arithmetic g

Arithmetic algebraic geometry is in a fascinating stage of growth, providing a rich variety of applications of new tools to both old and new problems. Represent

This book provides a self-contained proof of the Mordell conjecture (Faltings's theorem) and a concise introduction to Diophantine geometry.