Rational Points

Inhaltsverzeichnis

• 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.
• § 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.
• § 2 Preliminaries.
• § 3 The Tate-conjecture.
• § 4 The Shafarevich-conjecture.
• § 5 Endomorphisms.
• § 6 Effectivity.
• VII: Intersection Theory on Arithmetic Surfaces.
• § 1 Hermitian line bundies.
• § 2 Arakelov-divisors and intersection theory.
• § 3 Volume forms on IRr(X, ?).
• § 4 Riemann-Roch.
• § 5 The Hodge index theorem.