Diophantine Approximation and Abelian Varieties

Introductory Lectures

Bas Edixhoven, Jan-Hendrik Evertse (Herausgeber)

Buch | Softcover

XIV, 130 Seiten

1993 | 1993
Springer Berlin (Verlag)
978-3-540-57528-3 (ISBN)

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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.- 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).

Erscheint lt. Verlag	20.12.1993
Reihe/Serie	Lecture Notes in Mathematics
Zusatzinfo	XIV, 130 p.
Verlagsort	Berlin
Sprache	englisch
Maße	155 x 235 mm
Gewicht	222 g
Themenwelt	Mathematik / Informatik ► Mathematik ► Arithmetik / Zahlentheorie
	Mathematik / Informatik ► Mathematik ► Geometrie / Topologie
	Mathematik / Informatik ► Mathematik ► Wahrscheinlichkeit / Kombinatorik
Schlagworte	Abelian varieties • abelian variety • Abelsche Mannigfaltigkeit • Algebraic Geometry • Diophantine approximation • Diophantische Approximation • Grad • Number Theory
ISBN-10	3-540-57528-6 / 3540575286
ISBN-13	978-3-540-57528-3 / 9783540575283
Zustand	Neuware