Heights in Diophantine Geometry

Diophantine geometry has been studied for thousands of years, and it has inspired problems such as Fermat's Last Theorem and, more recently, the ABC conjecture. This monograph links the classical theory with the modern approach through arithmetic geometry.

The authors treat height functions, the central tool of the subject, and their use in problems such as the Mordell conjecture and the ABC conjecture. The opening chapters cover Weil heights, the product formula and heights on projective space, and later chapters move to the Mordell-Weil theorem and heights on abelian varieties.

Graduate students in number theory and algebraic geometry, and researchers who need a precise account of heights, are the intended audiences.

Edition note: published by Cambridge University Press. ISBN-13: 9780521712293.