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Fundamentals of diophantine geometry

Author: Serge Lang
Publisher: New York : Springer-Verlag, 1983.
Edition/Format:   eBook : Document : EnglishView all editions and formats
Summary:
Diophantine problems represent some of the strongest aesthetic attractions to algebraic geometry. They consist in giving criteria for the existence of solutions of algebraic equations in rings and fields, and eventually for the number of such solutions. The fundamental ring of interest is the ring of ordinary integers Z, and the fundamental field of interest is the field Q of rational numbers. One discovers rapidly  Read more...
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Genre/Form: Electronic books
Additional Physical Format: Print version:
Lang, Serge, 1927-2005.
Fundamentals of diophantine geometry
(DLC) 83000361
(OCoLC)9195763
Material Type: Document, Internet resource
Document Type: Internet Resource, Computer File
All Authors / Contributors: Serge Lang
ISBN: 9781475718102 1475718101 9781441928184 1441928189
OCLC Number: 861706324
Notes: "An earlier version of this book, Diophantine geometry, was published by Wiley-Interscience"--Title page verso.
Description: 1 online resource (xviii, 370 pages)
Contents: 1 Absolute Values --
2 Proper Sets of Absolute Values. Divisors and Units --
3 Heights --
4 Geometric Properties of Heights --
5 Heights on Abelian Varieties --
6 The Mordell-Weil Theorem --
7 The Thue-Siegel-Roth Theorem --
8 Siegel's Theorem and Integral Points --
9 Hilbert's Irreducibility Theorem --
10 Weil Functions and Néron Divisors --
11 Néron Functions on Abelian Varieties --
12 Algebraic Families of Néron Functions --
13 Néron Functions Over the Complex Numbers --
Review of S. Lang's Diophantine Geometry, by L.J. Mordell --
Review of L.J. Mordell's Diophantine Equations, by S. Lang.
Responsibility: Serge Lang.

Abstract:

The fundamental ring of interest is the ring of ordinary integers Z, and the fundamental field of interest is the field Q of rational numbers. Furthermore, one is led to consider also finite fields,  Read more...

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