ENGLISH

Logarithmic Forms and Diophantine Geometry

By A. Baker , G. Wüstholz

Book information

Publisher
Cambridge University Press
Year
2008
ISBN
0521882680, 9780521882682
Open Library ID
OL10438397M
Language
english
Format
PDF
Filesize
1 MB (1298177 bytes)
Series
New Mathematical Monographs
Edition
1
Pages
210\210
Time added
2011-01-06 10:13:16

Description

There is now much interplay between studies on logarithmic forms and deep aspects of arithmetic algebraic geometry. New light has been shed, for instance, on the famous conjectures of Tate and Shafarevich relating to abelian varieties and the associated celebrated discoveries of Faltings establishing the Mordell conjecture. This book gives an account of the theory of linear forms in the logarithms of algebraic numbers with special emphasis on the important developments of the past twenty-five years. The first part covers basic material in transcendental number theory but with a modern perspective. The remainder assumes some background in Lie algebras and group varieties, and covers, in some instances for the first time in book form, several advanced topics. The final chapter summarises other aspects of Diophantine geometry including hypergeometric theory and the André-Oort conjecture. A comprehensive bibliography rounds off this definitive survey of effective methods in Diophantine geometry.

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