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

This monograph presents new research on Arakelov geometry over adelic curves, a novel theory of arithmetic geometry developed by the authors. It explores positi

The main goal of this book is to present the so-called birational Arakelov geometry, which can be viewed as an arithmetic analog of the classical birational geo

An account for graduate students of this new technique in diophantine geometry; includes account of higher dimensional theory.

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