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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.
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.
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