Number Theory III
Diophantine Geometry
Authors: Lang, Serge
Editors: Lang, Serge (Ed.)
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- About this book
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From the reviews of the first printing of this book, published as Volume 60 of the Encyclopaedia of Mathematical Sciences: "Between number theory and geometry there have been several stimulating influences, and this book records of these enterprises. This author, who has been at the centre of such research for many years, is one of the best guides a reader can hope for. The book is full of beautiful results, open questions, stimulating conjectures and suggestions where to look for future developments.
This volume bears witness of the broad scope of knowledge of the author, and the influence of several people who have commented on the manuscript before publication ... Although in the series of number theory, this volume is on diophantine geometry, and the reader will notice that algebraic geometry is present in every chapter. ... The style of the book is clear. Ideas are well explained, and the author helps the reader to pass by several technicalities. Reading and rereading this book I noticed that the topics are treated in a nice, coherent way, however not in a historically logical order. ...The author writes "At the moment of writing, the situation is in flux...". That is clear from the scope of this book. In the area described many conjectures, important results, new developments took place in the last 30 years. And still new results come at a breathtaking speed in this rich field. In the introduction the author notices: "I have included several connections of diophantine geometry with other parts of mathematics, such as PDE and Laplacians, complex analysis, and differential geometry. A grand unification is going on, with multiple connections between these fields." Such a unification becomes clear in this beautiful book, which we recommend for mathematicians of all disciplines." Medelingen van het wiskundig genootschap, 1994
"... It is fascinating to see how geometry, arithmetic and complex analysis grow together!..." Monatshefte für Mathematik, 1993 - Reviews
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From the reviews: "Between number theory and geometry there have been several stimulating influences, and this book records these enterprises. This author, who has been at the centre of such research for many years, is one of the best guides a reader can hope for. The book is full of beautiful results, open questions, stimulating conjectures and suggestions where to look for future developments. This volume bears witness of the broad scope of knowledge of the author, and the influence of several people who have commented on the manuscript before publication... Although in the series of number theory, this volume is on diophantine geometry, the reader will notice that algebraic geometry is present in every chapter. ...The style of the book is clear. Ideas are well explained, and the author helps the reader to pass by several technicalities. Mededelingen van het wiskundig genootschap
- Table of contents (10 chapters)
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Some Qualitative Diophantine Statements
Pages 1-42
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Heights and Rational Points
Pages 43-67
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Abelian Varieties
Pages 68-100
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Faltings’ Finiteness Theorems on Abelian Varieties and Curves
Pages 101-122
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Modular Curves Over Q
Pages 123-142
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Table of contents (10 chapters)
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Bibliographic Information
- Bibliographic Information
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- Book Title
- Number Theory III
- Book Subtitle
- Diophantine Geometry
- Authors
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- Serge Lang
- Editors
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- Serge Lang
- Series Title
- Encyclopaedia of Mathematical Sciences
- Series Volume
- 60
- Copyright
- 1991
- Publisher
- Springer-Verlag Berlin Heidelberg
- Copyright Holder
- Springer-Verlag Berlin Heidelberg
- eBook ISBN
- 978-3-642-58227-1
- DOI
- 10.1007/978-3-642-58227-1
- Hardcover ISBN
- 978-3-540-53004-6
- Softcover ISBN
- 978-3-540-61223-0
- Series ISSN
- 0938-0396
- Edition Number
- 1
- Number of Pages
- XIII, 296
- Additional Information
- Originally published as volume 60 in the series Encyclopaedia of Mathematical Sciences with the title: Number Theory 3
- Topics
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