Diophantine Approximation and Abelian Varieties Introductory Lectures [Paperback]

The 13 chapters of this book centre around the proof ofTheorem 1 of Faltings' paper Diophantine approximation onabelian varieties , Ann. Math.133 (1991) and together givean approach to the proof that is accessible to Ph.D-levelstudents in number theory and algebraic geometry. Eachchapter is based on an instructional lecture given by itsauthor ata special conference for graduate students, on thetopic of Faltings' paper.The 13 chapters of this book centre around the proof ofTheorem 1 of Faltings' paper Diophantine approximation onabelian varieties , Ann. Math.133 (1991) and together givean approach to the proof that is accessible to Ph.D-levelstudents in number theory and algebraic geometry. Eachchapter is based on an instructional lecture given by itsauthor ata special conference for graduate students, on thetopic of Faltings' paper.Diophantine Equations and Approximation.- Diophantine Approximation and its Applications.- Roths Theorem.- The Subspace Theorem of W.M. Schmidt.- Heights on Abelian Varieties.- D. Mumfords A Remark on Mordells Conjecture.- Ample Line Bundles and Intersection Theory.- The Product Theorem.- Geometric Part of Faltingss Proof.- Faltingss Version of Siegels Lemma.- Arithmetic Part of Faltingss Proof.- Points of Degree d on Curves over Number Fields.- The General Case of S. Langs Conjecture (after Faltings).Springer Book Archives