Rational points

InhaltsverzeichnisI: 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.