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