[PDF] Diophantine Approximation And Abelian Varieties eBook

Author : Bas Edixhoven
Publisher : Springer
Page : 136 pages
File Size : 47,48 MB
Release : 2009-02-05
Category : Mathematics
ISBN : 3540482083

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The 13 chapters of this book centre around the proof of Theorem 1 of Faltings' paper "Diophantine approximation on abelian varieties", Ann. Math.133 (1991) and together give an approach to the proof that is accessible to Ph.D-level students in number theory and algebraic geometry. Each chapter is based on an instructional lecture given by its author ata special conference for graduate students, on the topic of Faltings' paper.

Author : Min Ru
Publisher : World Scientific
Page : 443 pages
File Size : 35,43 MB
Release : 2021-03-10
Category : Mathematics
ISBN : 9811233527

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This book describes the theories and developments in Nevanlinna theory and Diophantine approximation. Although these two subjects belong to the different areas: one in complex analysis and one in number theory, it has been discovered that a number of striking similarities exist between these two subjects. A growing understanding of these connections has led to significant advances in both fields. Outstanding conjectures from decades ago are being solved.Over the past 20 years since the first edition appeared, there have been many new and significant developments. The new edition greatly expands the materials. In addition, three new chapters were added. In particular, the theory of algebraic curves, as well as the algebraic hyperbolicity, which provided the motivation for the Nevanlinna theory.

Author : Jan-Hendrik Evertse
Publisher : Cambridge University Press
Page : 381 pages
File Size : 34,24 MB
Release : 2015-12-30
Category : Mathematics
ISBN : 1316432351

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Diophantine number theory is an active area that has seen tremendous growth over the past century, and in this theory unit equations play a central role. This comprehensive treatment is the first volume devoted to these equations. The authors gather together all the most important results and look at many different aspects, including effective results on unit equations over number fields, estimates on the number of solutions, analogues for function fields and effective results for unit equations over finitely generated domains. They also present a variety of applications. Introductory chapters provide the necessary background in algebraic number theory and function field theory, as well as an account of the required tools from Diophantine approximation and transcendence theory. This makes the book suitable for young researchers as well as experts who are looking for an up-to-date overview of the field.

Author : Marc Hindry
Publisher : Springer Science & Business Media
Page : 574 pages
File Size : 39,32 MB
Release : 2013-12-01
Category : Mathematics
ISBN : 1461212103

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This is an introduction to diophantine geometry at the advanced graduate level. The book contains a proof of the Mordell conjecture which will make it quite attractive to graduate students and professional mathematicians. In each part of the book, the reader will find numerous exercises.