UID:
almahu_9947363165902882
Format:
XI, 312 p.
,
online resource.
Edition:
Third Enlarged Edition.
ISBN:
9783322803405
Series Statement:
Aspects of Mathematics, 6
Note:
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 -- § 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 to Mordell -- § 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 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.
In:
Springer eBooks
Additional Edition:
Printed edition: ISBN 9783322803429
Language:
English
Keywords:
Konferenzschrift
;
Konferenzschrift
DOI:
10.1007/978-3-322-80340-5
URL:
http://dx.doi.org/10.1007/978-3-322-80340-5
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