Gerd Faltings

Rational Points

Seminar Bonn/Wuppertal 1983/84 A Publication of the Max-Planck-Institut für Mathematik, Bonn

• Broschiertes Buch

Produktdetails

• Verlag: Vieweg+Teubner / Vieweg+Teubner Verlag
• Artikelnr. des Verlages: 978-3-528-08593-3
• 1984.
• Seitenzahl: 280
• Erscheinungstermin: 1. Januar 1984
• Deutsch
• Abmessung: 244mm x 170mm x 16mm
• Gewicht: 488g
• ISBN-13: 9783528085933
• ISBN-10: 3528085932
• Artikelnr.: 32004520

Inhaltsangabe

I: Moduli Spaces.-
1 Introduction.-
2 Generalities about moduli-Spaces.-
3 Examples.-
4 Metrics with logarithmic singularities.-
5 The minimal compact if ication of Ag/?.-
6 The toroidal compactification.- II: Heights.-
1 The definition.-
2 Néron-Tate heights.-
3 Heights on the moduli-space.-
4 Applications.- III: Some Facts from the Theory of Group Schemes.-
0 Introduction.-
1 Generalities on group schemes.-
2 Finite group schemes.-
3 p-divisible groups.-
4 A theorem of Raynaud.-
5 A theorem of Tate.- IV: Tate's Conjecture on the Endomorphisms of Abelian Varieties.-
1 Statements.-
2 Reductions.-
3 Heights.-
4 Variants.- V: The Finiteness Theorems of Faltings.-
1 Introduction.-
2 The finiteness theorem for isogeny classes.-
3 The finiteness theorem for isomorphism classes.-
4 Proof of Mordell's conjecture.-
5 Siegel's Theorem on integer points.- VI: Complements.-
1 Introduction.-
2 Preliminaries.-
3 The Tate-conjecture.-
4 The Shafarevich-conjecture.-
5 Endomorphisms.-
6 Effectivity.- VII: Intersection Theory on Arithmetic Surfaces.-
0 Introduction.-
1 Hermitian line bundies.-
2 Arakelov-divisors and intersection theory.-
3 Volume forms on IRr(X, ?).-
4 Riemann-Roch.-
5 The Hodge index theorem.