Heights in Diophantine Geometry [Paperback]

This monograph is a bridge between the classical theory and modern approach via arithmetic geometry.Diophantine geometry has been studied by number theorists for thousands of years. This monograph is a bridge between the classical theory and modern approach via arithmetic geometry. The authors provide a clear path through the subject for graduate students and researchers. They have re-examined many results and much of the literature, and give a thorough account of several topics at a level not seen before in book form. The treatment is largely self-contained, with proofs given in full detail. Many results appear here for the first time.Diophantine geometry has been studied by number theorists for thousands of years. This monograph is a bridge between the classical theory and modern approach via arithmetic geometry. The authors provide a clear path through the subject for graduate students and researchers. They have re-examined many results and much of the literature, and give a thorough account of several topics at a level not seen before in book form. The treatment is largely self-contained, with proofs given in full detail. Many results appear here for the first time.Diophantine geometry has been studied by number theorists for thousands of years, since the time of Pythagoras, and has continued to be a rich area of ideas such as Fermat's Last Theorem, and most recently the ABC conjecture. This monograph is a bridge between the classical theory and modern approach via arithmetic geometry. The authors provide a clear path through the subject for graduate students and researchers. They have re-examined many results and much of the literature, and provide a thorough account of several topics at a level not seen before in book form. The treatment is largely self-contained, with proofs given in full detail.1. Heights; 2. Weil heights; 3. Linear tori; 4. Small points; 5. The unit equation; 6. Roth's theorem; 7. The subspace theorem; 8. Abelian varieties; 9. Neron-Tate lÓE