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Catalogue Information
Field name	Details
Dewey Class	512.7
Title	Rational Points ([EBook] :) : Seminar Bonn/Wuppertal 1983/84 / / by Gerd Faltings, Gisbert Wüstholz.
Author	Faltings, Gerd
Added Personal Name	Wüstholz, Gisbert author.
Other name(s)	SpringerLink (Online service)
Edition statement	Third Enlarged Edition.
Publication	Wiesbaden : : Vieweg+Teubner Verlag, , 1992.
Physical Details	XI, 312 p. : online resource.
Series	Aspects of mathematics 0179-2156 ; ; 6
ISBN	9783322803405
Contents 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.
System details note	Online access to this digital book is restricted to subscription institutions through IP address (only for SISSA internal users)
Internet Site	http://dx.doi.org/10.1007/978-3-322-80340-5
Links to Related Works	Subject References: Difference and Functional Equations . Difference equations . Functional equations . Geometry . Mathematics . Number Theory . Authors: Faltings, Gerd . Wüstholz, Gisbert . Corporate Authors: SpringerLink (Online service) . Series: Aspects of mathematics . Classification: 512.7 .

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Rational Points: Seminar Bonn/Wuppertal 1983/84 /

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