The Mordell conjecture (Faltings's theorem) is one of the most important achievements in Diophantine geometry, stating that an algebraic curve of genus at least

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

The book is based on a course given by J.-P. Serre at the Collège de France in 1980 and 1981. Basic techniques in Diophantine geometry are covered, such as hei

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 Dynamical Mordell-Lang Conjecture is an analogue of the classical Mordell-Lang conjecture in the context of arithmetic dynamics. It predicts the behavior of