Heights In Diophantine Geometry

Author : Enrico Bombieri
Publisher : Cambridge University Press
ISBN 13 : 1139447955
Total Pages : 73 pages
Book Rating : 4.59/5 ( download)

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Download or read book Heights in Diophantine Geometry written by Enrico Bombieri and published by Cambridge University Press. This book was released on 2007-09-06 with total page 73 pages. Available in PDF, EPUB and Kindle. Book excerpt: Diophantine geometry has been studied by number theorists for thousands of years, this monograph is a bridge between the classical theory and modern approach via arithmetic geometry. The treatment is largely self-contained, with proofs given in full detail. Many results appear here for the first time.

Author : Marc Hindry
Publisher : Springer Science & Business Media
ISBN 13 : 1461212103
Total Pages : 574 pages
Book Rating : 4.02/5 ( download)

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Download or read book Diophantine Geometry written by Marc Hindry and published by Springer Science & Business Media. This book was released on 2013-12-01 with total page 574 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

Author : Enrico Bombieri
Publisher :
ISBN 13 :
Total Pages : 652 pages
Book Rating : 4.04/5 ( download)

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Download or read book Heights in Diophantine Geometry written by Enrico Bombieri and published by . This book was released on 2006 with total page 652 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Author : Enrico Bombieri
Publisher : Cambridge University Press
ISBN 13 : 9780521712293
Total Pages : 676 pages
Book Rating : 4.97/5 ( download)

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Download or read book Heights in Diophantine Geometry written by Enrico Bombieri and published by Cambridge University Press. This book was released on 2006 with total page 676 pages. Available in PDF, EPUB and Kindle. Book excerpt: This monograph is a bridge between the classical theory and modern approach via arithmetic geometry.

Author : Enrico Bombieri
Publisher :
ISBN 13 : 9780521169929
Total Pages : pages
Book Rating : 4.25/5 ( download)

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Download or read book Heights in Diophantine Geometry ICM Edition written by Enrico Bombieri and published by . This book was released on 2010-07-23 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt:

Author : S. Lang
Publisher : Springer Science & Business Media
ISBN 13 : 1475718101
Total Pages : 383 pages
Book Rating : 4.02/5 ( download)

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Download or read book Fundamentals of Diophantine Geometry written by S. Lang and published by Springer Science & Business Media. This book was released on 2013-06-29 with total page 383 pages. Available in PDF, EPUB and Kindle. Book excerpt: Diophantine problems represent some of the strongest aesthetic attractions to algebraic geometry. They consist in giving criteria for the existence of solutions of algebraic equations in rings and fields, and eventually for the number of such solutions. The fundamental ring of interest is the ring of ordinary integers Z, and the fundamental field of interest is the field Q of rational numbers. One discovers rapidly that to have all the technical freedom needed in handling general problems, one must consider rings and fields of finite type over the integers and rationals. Furthermore, one is led to consider also finite fields, p-adic fields (including the real and complex numbers) as representing a localization of the problems under consideration. We shall deal with global problems, all of which will be of a qualitative nature. On the one hand we have curves defined over say the rational numbers. Ifthe curve is affine one may ask for its points in Z, and thanks to Siegel, one can classify all curves which have infinitely many integral points. This problem is treated in Chapter VII. One may ask also for those which have infinitely many rational points, and for this, there is only Mordell's conjecture that if the genus is :;;; 2, then there is only a finite number of rational points.

Author : Hideaki Ikoma
Publisher : Cambridge University Press
ISBN 13 : 1108845959
Total Pages : 179 pages
Book Rating : 4.53/5 ( download)

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Download or read book The Mordell Conjecture written by Hideaki Ikoma and published by Cambridge University Press. This book was released on 2022-02-03 with total page 179 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book provides a self-contained proof of the Mordell conjecture (Faltings's theorem) and a concise introduction to Diophantine geometry.

Author : Emmanuel Peyre
Publisher : Springer Nature
ISBN 13 : 3030575594
Total Pages : 469 pages
Book Rating : 4.95/5 ( download)

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Download or read book Arakelov Geometry and Diophantine Applications written by Emmanuel Peyre and published by Springer Nature. This book was released on 2021-03-10 with total page 469 pages. Available in PDF, EPUB and Kindle. Book excerpt: Bridging the gap between novice and expert, the aim of this book is to present in a self-contained way a number of striking examples of current diophantine problems to which Arakelov geometry has been or may be applied. Arakelov geometry can be seen as a link between algebraic geometry and diophantine geometry. Based on lectures from a summer school for graduate students, this volume consists of 12 different chapters, each written by a different author. The first chapters provide some background and introduction to the subject. These are followed by a presentation of different applications to arithmetic geometry. The final part describes the recent application of Arakelov geometry to Shimura varieties and the proof of an averaged version of Colmez's conjecture. This book thus blends initiation to fundamental tools of Arakelov geometry with original material corresponding to current research. This book will be particularly useful for graduate students and researchers interested in the connections between algebraic geometry and number theory. The prerequisites are some knowledge of number theory and algebraic geometry.

Author : Wolfgang M. Schmidt
Publisher : Springer
ISBN 13 : 3540473742
Total Pages : 224 pages
Book Rating : 4.49/5 ( download)

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Download or read book Diophantine Approximations and Diophantine Equations written by Wolfgang M. Schmidt and published by Springer. This book was released on 2006-12-08 with total page 224 pages. Available in PDF, EPUB and Kindle. Book excerpt: "This book by a leading researcher and masterly expositor of the subject studies diophantine approximations to algebraic numbers and their applications to diophantine equations. The methods are classical, and the results stressed can be obtained without much background in algebraic geometry. In particular, Thue equations, norm form equations and S-unit equations, with emphasis on recent explicit bounds on the number of solutions, are included. The book will be useful for graduate students and researchers." (L'Enseignement Mathematique) "The rich Bibliography includes more than hundred references. The book is easy to read, it may be a useful piece of reading not only for experts but for students as well." Acta Scientiarum Mathematicarum

Author : R. C. Mason
Publisher : Cambridge University Press
ISBN 13 : 9780521269834
Total Pages : 142 pages
Book Rating : 4.30/5 ( download)

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Download or read book Diophantine Equations Over Function Fields written by R. C. Mason and published by Cambridge University Press. This book was released on 1984-04-26 with total page 142 pages. Available in PDF, EPUB and Kindle. Book excerpt: A self-contained account of a new approach to the subject.