Diophantine Approximation and Abelian Varieties: Introductory Lectures

ISBN-13: 9783540575283 / Angielski / Miękka / 1993 / 130 str.

Bas Edixhoven; Jan-Hendrik Evertse; B. Edixhoven

Opis

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.

Spis treści

Diophantine Equations and Approximation.- Diophantine Approximation and its Applications.- Roth’s Theorem.- The Subspace Theorem of W.M. Schmidt.- Heights on Abelian Varieties.- D. Mumford’s “A Remark on Mordell’s Conjecture”.- Ample Line Bundles and Intersection Theory.- The Product Theorem.- Geometric Part of Faltings’s Proof.- Faltings’s Version of Siegel’s Lemma.- Arithmetic Part of Faltings’s Proof.- Points of Degree d on Curves over Number Fields.- “The” General Case of S. Lang’s Conjecture (after Faltings).