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Inhaltsverzeichnis
- I: Moduli Spaces.
- § 1 Introduction.
- § 2 Generalities about moduli spaces.
- § 3 Examples.
- § 4 Metrics with logarithmic singularities.
- § 5 The minimal compactification of Ag/?.
- § 8 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.
- § 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 to Mordell.
- § 2 Preliminaries.
- § 3 The Tate conjecture.
- § 4 The Shafarevich conjecture.
- § 5 Endomorphisms.
- § 6 Effectivity.
- VII: Intersection Theory on Arithmetic Surfaces.
- § 1 Hermitian line bundles.
- § 2 Arakelov divisors and intersection theory.
- § 3 Volume forms on IR?(X, ?).
- § 4 Riemann Roch.
- § 5 The Hodge index theorem.
- Appendix: New Developments in Diophantine and Arithmetic Algebraic Geometry (Gisbert Wüstholz).
- § 2 The transcendental approach.
- § 3 Vojta’s approach.
- § 4 Arithmetic Riemann-Roch Theorem.
- § 5 Applications in Arithmetic.
- § 6 Small sections.
- § 7 Vojta’s proof in the number field case.
- § 8 Lang’s conjecture.
- § 9 Proof of Faltings’ theorem.
- § 10 An elementary proof of Mordell’s conjecture.
- § 11 ?-adic representations attached to abelian varieties.
