Format:
1 online resource (x, 198 pages)
ISBN:
9780521882682
,
9780511542862
Series Statement:
New mathematical monographs 9
Content:
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.
Content:
Transcendence origins -- Logarithmic forms -- Diophantine problems -- Commutative algebraic groups -- Multiplicity estimates -- The analytic subgroup theorem -- The quantitative theory -- Further aspects of diophantine geometry
Note:
Title from publisher's bibliographic system (viewed on 05 Oct 2015)
Additional Edition:
ISBN 9780521882682
Additional Edition:
Baker, Alan, 1939 - 2018 Logarithmic forms and diophantine geometry Cambridge [u.a.] : Cambridge Univ. Press, 2007 ISBN 0521882680
Additional Edition:
ISBN 9780521882682
Additional Edition:
Erscheint auch als Druck-Ausgabe ISBN 9780521882682
Language:
English
Subjects:
Mathematics
Keywords:
Diophantische Geometrie
;
Arithmetische Geometrie
;
Logarithmus
DOI:
10.1017/CBO9780511542862
Author information:
Wüstholz, Gisbert 1948-
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