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Cover: 9780521882682 | Logarithmic Forms and Diophantine Geometry | A. Baker (u. a.) | Buch
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Logarithmic Forms and Diophantine Geometry
Buch von A. Baker (u. a.)
Sprache: Englisch

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Beschreibung
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.
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.
Über den Autor
Alan Baker ,FRS, is Emeritus Professor of Pure Mathematics in the University of Cambridge and Fellow of Trinity College, Cambridge. He has received numerous international awards, including, in 1970, a Fields medal for his work in number theory. This is his third authored book: he has edited four others for publication.
Zusammenfassung
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. A comprehensive bibliography rounds off this definitive survey of effective methods in Diophantine geometry.
Inhaltsverzeichnis
Preface. 1. Transcendence origins; 2. Logarithmic forms; 3. Diophantine problems; 4. Commutative algebraic groups; 5. Multiplicity estimates; 6. The analytic subgroup theorem; 7. The quantitative theory; 8. Further aspects of Diophantine geometry; Bibliography; Index.
Details
Erscheinungsjahr: 2008
Fachbereich: Allgemeines
Genre: Importe, Mathematik
Rubrik: Naturwissenschaften & Technik
Medium: Buch
ISBN-13: 9780521882682
ISBN-10: 0521882680
Sprache: Englisch
Einband: Gebunden
Autor: Baker, A.
Wüstholz, G.
Hersteller: Cambridge University Press
Verantwortliche Person für die EU: Libri GmbH, Europaallee 1, D-36244 Bad Hersfeld, gpsr@libri.de
Maße: 235 x 157 x 17 mm
Von/Mit: A. Baker (u. a.)
Erscheinungsdatum: 17.01.2008
Gewicht: 0,499 kg
Artikel-ID: 123686621
Über den Autor
Alan Baker ,FRS, is Emeritus Professor of Pure Mathematics in the University of Cambridge and Fellow of Trinity College, Cambridge. He has received numerous international awards, including, in 1970, a Fields medal for his work in number theory. This is his third authored book: he has edited four others for publication.
Zusammenfassung
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. A comprehensive bibliography rounds off this definitive survey of effective methods in Diophantine geometry.
Inhaltsverzeichnis
Preface. 1. Transcendence origins; 2. Logarithmic forms; 3. Diophantine problems; 4. Commutative algebraic groups; 5. Multiplicity estimates; 6. The analytic subgroup theorem; 7. The quantitative theory; 8. Further aspects of Diophantine geometry; Bibliography; Index.
Details
Erscheinungsjahr: 2008
Fachbereich: Allgemeines
Genre: Importe, Mathematik
Rubrik: Naturwissenschaften & Technik
Medium: Buch
ISBN-13: 9780521882682
ISBN-10: 0521882680
Sprache: Englisch
Einband: Gebunden
Autor: Baker, A.
Wüstholz, G.
Hersteller: Cambridge University Press
Verantwortliche Person für die EU: Libri GmbH, Europaallee 1, D-36244 Bad Hersfeld, gpsr@libri.de
Maße: 235 x 157 x 17 mm
Von/Mit: A. Baker (u. a.)
Erscheinungsdatum: 17.01.2008
Gewicht: 0,499 kg
Artikel-ID: 123686621
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