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Viser: Diophantine Geometry - An Introduction
Diophantine Geometry
An Introduction
Marc Hindry og Joseph H. Silverman
(2000)
Sprog: Engelsk
om ca. 10 hverdage
Detaljer om varen
- 1. Udgave
- Hardback
- Udgiver: Springer New York (Marts 2000)
- Forfattere: Marc Hindry og Joseph H. Silverman
- ISBN: 9780387989754
1.- D.9 Application: Integer Points on Curves.- Exercises.- E Rational Points on Curves of Genus at Least
2.- E.I Vojta's Geometric Inequality and Faltings' Theorem.- E.2 Pinning Down Some Height Functions.- E.3 An Outline of the Proof of Vojta's Inequality.- E.4 An Upper Bound for h?(z, w).- E.5 A Lower Bound for h?(z,w) for Nonvanishing Sections.- E.6 Constructing Sections of Small Height I: Applying Riemann--Roch.- E.7 Constructing Sections of Small Height II: Applying Siegel's Lemma.- E.8 Lower Bound for h?(z,w) at Admissible Version I.- E.9 Eisenstein's Estimate for the Derivatives of an Algebraic Function.- E.10 Lower Bound for h?(z,w) at Admissible: Version II.- E.11 A Nonvanishing Derivative of Small Order.- E.12 Completion of the Proof of Vojta's Inequality.- Exercises.- F Further Results and Open Problems.- F.1 Curves and Abelian Varieties.- F.2 Discreteness of Algebraic Points.- F.3 Height Bounds and Height Conjectures.- F.4 The Search for Effectivity.- F.5 Geometry Governs Arithmetic.- Exercises.- References.- List of Notation.