Diophantine Approximation and Abelian Varieties

Introductory Lectures
1993
ISBN: 978-3-540-57528-3
Verlag: Springer Berlin Heidelberg

Buch, Englisch, Band 1566, 130 Seiten, Format (B × H): 155 mm x 235 mm, Gewicht: 230 g

Reihe: Lecture Notes in Mathematics

The 13 chapters of this book centre around the proof of
Theorem 1 of Faltings' paper "Diophantine approximation on
abelian varieties", Ann. Math.133 (1991) and together give
an approach to the proof that is accessible to Ph.D-level
students in number theory and algebraic geometry. Each
chapter is based on an instructional lecture given by its
author ata special conference for graduate students, on the
topic of Faltings' paper.

Zielgruppe

Research

Autoren/Hrsg.

Evertse, Jan-Hendrik

Edixhoven, Bas

Fachgebiete

• Mathematik | Informatik Mathematik Algebra Zahlentheorie
• Mathematik | Informatik Mathematik Geometrie Algebraische Geometrie

Inhaltsverzeichnis

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).