ENGLISH

Number theory 3: Diophantine geometry

By Serge Lang

Book information

Publisher
Springer
Year
1991
ISBN
9780387530048, 9783540530046, 3540530045, 0387530045
LCC
QA242 .N85 1991
Open Library ID
OL1539217M
Language
english
Format
DJVU
Filesize
2 MB (1848028 bytes)
Series
Encyclopaedia of Mathematical Sciences 60
Edition
1
Pages
304\304
Library
Kolxo3
DPI
300
Time added
2009-12-04 00:34:26

Description

Diophantine problems concern the solutions of equations in integers, rational numbers, or various generalizations. The book is an encyclopedic survey of diophantine geometry. For the most part no proofs are given, but references are given where proofs may be found. There are some exceptions, notably the proof for a large part of Faltings' theorems is given. The survey puts together, from a unified point of view, the field of diophantine geometry which has developed since the early 1950's, after its origins in Mordell, Weil and Siegel's papers in the 1920's. The basic approach is that of algebraic geometry, but examples are given which show how this approach deals with (and sometimes solves!) classical problems phrased in very elementary terms. For instance, the Fermat problem is not solved, but it is shown to fit in to two great structural approaches, so that it is not an isolated problem any more.

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