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Diophantine Approximation And Abelian Varieties


Diophantine Approximation And Abelian Varieties
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Diophantine Approximation And Abelian Varieties


Diophantine Approximation And Abelian Varieties
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Author : Bas Edixhoven
language : en
Publisher: Springer Science & Business Media
Release Date : 1993-12-20

Diophantine Approximation And Abelian Varieties written by Bas Edixhoven and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 1993-12-20 with Mathematics categories.


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.



Diophantine Approximation And Abelian Varieties


Diophantine Approximation And Abelian Varieties
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Author :
language : en
Publisher:
Release Date : 1993

Diophantine Approximation And Abelian Varieties written by and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1993 with categories.




Diophantine Approximation And Abelian Varieties


Diophantine Approximation And Abelian Varieties
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Author : Bas Edixhoven
language : en
Publisher:
Release Date : 2014-01-15

Diophantine Approximation And Abelian Varieties written by Bas Edixhoven and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-01-15 with categories.




Effective Diophantine Approximation On Abelian Varieties I


Effective Diophantine Approximation On Abelian Varieties I
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Author : Eric Gaudron
language : en
Publisher:
Release Date : 2002

Effective Diophantine Approximation On Abelian Varieties I written by Eric Gaudron and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2002 with categories.




Diophantine Approximation And Abelian Varieties


Diophantine Approximation And Abelian Varieties
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Author : Frits Beukers
language : en
Publisher:
Release Date : 1992

Diophantine Approximation And Abelian Varieties written by Frits Beukers and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1992 with Diophantine approximation categories.




A Dynamical Counterpart To Falting S Diophantine Approximation On Abelian Varieties


A Dynamical Counterpart To Falting S Diophantine Approximation On Abelian Varieties
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Author : Michael McQuillan
language : en
Publisher:
Release Date : 1996

A Dynamical Counterpart To Falting S Diophantine Approximation On Abelian Varieties written by Michael McQuillan and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1996 with categories.




Nevanlinna Theory And Its Relation To Diophantine Approximation Second Edition


Nevanlinna Theory And Its Relation To Diophantine Approximation Second Edition
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Author : Min Ru
language : en
Publisher: World Scientific
Release Date : 2021-03-10

Nevanlinna Theory And Its Relation To Diophantine Approximation Second Edition written by Min Ru and has been published by World Scientific this book supported file pdf, txt, epub, kindle and other format this book has been release on 2021-03-10 with Mathematics categories.


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.



Diophantine Approximation And Abelian Varieties


Diophantine Approximation And Abelian Varieties
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Author : Bas Edixhoven
language : en
Publisher: Springer
Release Date : 2003-05-22

Diophantine Approximation And Abelian Varieties written by Bas Edixhoven and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2003-05-22 with Mathematics categories.


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.



Diophantine Geometry


Diophantine Geometry
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Author : Marc Hindry
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-12-01

Diophantine Geometry written by Marc Hindry and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-12-01 with Mathematics categories.


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.



Nevanlinna Theory In Several Complex Variables And Diophantine Approximation


Nevanlinna Theory In Several Complex Variables And Diophantine Approximation
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Author : Junjiro Noguchi
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-12-09

Nevanlinna Theory In Several Complex Variables And Diophantine Approximation written by Junjiro Noguchi and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-12-09 with Mathematics categories.


The aim of this book is to provide a comprehensive account of higher dimensional Nevanlinna theory and its relations with Diophantine approximation theory for graduate students and interested researchers. This book with nine chapters systematically describes Nevanlinna theory of meromorphic maps between algebraic varieties or complex spaces, building up from the classical theory of meromorphic functions on the complex plane with full proofs in Chap. 1 to the current state of research. Chapter 2 presents the First Main Theorem for coherent ideal sheaves in a very general form. With the preparation of plurisubharmonic functions, how the theory to be generalized in a higher dimension is described. In Chap. 3 the Second Main Theorem for differentiably non-degenerate meromorphic maps by Griffiths and others is proved as a prototype of higher dimensional Nevanlinna theory. Establishing such a Second Main Theorem for entire curves in general complex algebraic varieties is a wide-open problem. In Chap. 4, the Cartan-Nochka Second Main Theorem in the linear projective case and the Logarithmic Bloch-Ochiai Theorem in the case of general algebraic varieties are proved. Then the theory of entire curves in semi-abelian varieties, including the Second Main Theorem of Noguchi-Winkelmann-Yamanoi, is dealt with in full details in Chap. 6. For that purpose Chap. 5 is devoted to the notion of semi-abelian varieties. The result leads to a number of applications. With these results, the Kobayashi hyperbolicity problems are discussed in Chap. 7. In the last two chapters Diophantine approximation theory is dealt with from the viewpoint of higher dimensional Nevanlinna theory, and the Lang-Vojta conjecture is confirmed in some cases. In Chap. 8 the theory over function fields is discussed. Finally, in Chap. 9, the theorems of Roth, Schmidt, Faltings, and Vojta over number fields are presented and formulated in view of Nevanlinna theory with results motivated by those in Chaps. 4, 6, and 7.