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＜電子ブック＞
Rational Points : Seminar Bonn/Wuppertal 1983/84 / by Gerd Faltings, Gisbert Wüstholz
(Aspects of Mathematics ; 6)

版	3rd ed. 1992.
出版者	(Wiesbaden : Vieweg+Teubner Verlag : Imprint: Vieweg+Teubner Verlag)
出版年	1992
本文言語	英語
大きさ	XI, 312 p : online resource
著者標目	*Faltings, Gerd author Wüstholz, Gisbert author SpringerLink (Online service)
件　名	LCSH:Number theory LCSH:Geometry LCSH:Difference equations LCSH:Functional equations FREE:Number Theory FREE:Geometry FREE:Difference and Functional Equations
一般注記	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 HTTP:URL=https://doi.org/10.1007/978-3-322-80340-5

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