Fundamentals Of Diophantine Geometry
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Fundamentals Of Diophantine Geometry
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Author : S. Lang
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-06-29
Fundamentals Of Diophantine Geometry written by S. Lang 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 2013-06-29 with Mathematics categories.
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.
Fundamentals Of Diophantine Geometry
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Author : Serge Lang
language : en
Publisher:
Release Date : 1983-01-01
Fundamentals Of Diophantine Geometry written by Serge Lang and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1983-01-01 with Arithmetical algebraic geometry categories.
Number Theory Iii
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Author : Serge Lang
language : en
Publisher: Springer Science & Business Media
Release Date : 1997-04-14
Number Theory Iii written by Serge Lang 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 1997-04-14 with Mathematics categories.
In 1988 Shafarevich asked me to write a volume for the Encyclopaedia of Mathematical Sciences on Diophantine Geometry. I said yes, and here is the volume. By definition, diophantine problems concern the solutions of equations in integers, or rational numbers, or various generalizations, such as finitely generated rings over Z or finitely generated fields over Q. The word Geometry is tacked on to suggest geometric methods. This means that the present volume is not elementary. For a survey of some basic problems with a much more elementary approach, see [La 9Oc]. The field of diophantine geometry is now moving quite rapidly. Out standing conjectures ranging from decades back are being proved. I have tried to give the book some sort of coherence and permanence by em phasizing structural conjectures as much as results, so that one has a clear picture of the field. On the whole, I omit proofs, according to the boundary conditions of the encyclopedia. On some occasions I do give some ideas for the proofs when these are especially important. In any case, a lengthy bibliography refers to papers and books where proofs may be found. I have also followed Shafarevich's suggestion to give examples, and I have especially chosen these examples which show how some classical problems do or do not get solved by contemporary in sights. Fermat's last theorem occupies an intermediate position. Al though it is not proved, it is not an isolated problem any more.
Diophantine Geometry
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Author : Serge Lang
language : en
Publisher:
Release Date : 1962
Diophantine Geometry written by Serge Lang and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1962 with Diophantine analysis categories.
Diophantine Geometry
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Author : Serge Lang
language : en
Publisher: Hassell Street Press
Release Date : 2021-09-09
Diophantine Geometry written by Serge Lang and has been published by Hassell Street Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2021-09-09 with Mathematics categories.
This work has been selected by scholars as being culturally important and is part of the knowledge base of civilization as we know it. This work is in the public domain in the United States of America, and possibly other nations. Within the United States, you may freely copy and distribute this work, as no entity (individual or corporate) has a copyright on the body of the work. Scholars believe, and we concur, that this work is important enough to be preserved, reproduced, and made generally available to the public. To ensure a quality reading experience, this work has been proofread and republished using a format that seamlessly blends the original graphical elements with text in an easy-to-read typeface. We appreciate your support of the preservation process, and thank you for being an important part of keeping this knowledge alive and relevant.
Diophantine Geometry
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Author : Umberto Zannier
language : en
Publisher: Springer
Release Date : 2007-06-27
Diophantine Geometry written by Umberto Zannier and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2007-06-27 with Mathematics categories.
This book contains research articles on Diophantine Geometry, written by participants of a research program held at the Ennio De Giorgi Mathematical Research Center in Pisa, Italy, between April and July 2005. The authors are eminent experts in the field and present several subfields of the main topic. The volume provides a broad overview of recent research developments.
Diophantine Discoveries Fundamentals
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Author : N.B. Singh
language : en
Publisher: N.B. Singh
Release Date :
Diophantine Discoveries Fundamentals written by N.B. Singh and has been published by N.B. Singh this book supported file pdf, txt, epub, kindle and other format this book has been release on with Mathematics categories.
"Diophantine Discoveries Fundamentals" is a beginner-friendly exploration of the captivating world of Diophantine equations, designed for those with no prior mathematical background. Delving into the realm of mathematical puzzles, this book offers clear and accessible explanations of Diophantine equations, starting from the basics and gradually building up the reader's understanding. Through engaging examples and straightforward language, readers are introduced to the fascinating concepts of finding whole number solutions to polynomial equations. From the historical significance of Diophantine equations to their applications in various fields such as number theory, algebra, and cryptography, this book serves as an inviting gateway for curious minds to unravel the mysteries of mathematics. Whether you're a student eager to expand your mathematical knowledge or simply someone with a passion for learning, "Diophantine Discoveries Fundamentals" provides an enjoyable and educational journey into the heart of mathematical exploration.
Heights In Diophantine Geometry
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Author : Enrico Bombieri
language : en
Publisher: Cambridge University Press
Release Date : 2007-09-06
Heights In Diophantine Geometry written by Enrico Bombieri and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2007-09-06 with Mathematics categories.
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.
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.
Integral Points On Algebraic Varieties
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Author : Pietro Corvaja
language : en
Publisher:
Release Date : 2016
Integral Points On Algebraic Varieties written by Pietro Corvaja and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2016 with Arithmetical algebraic geometry categories.
Offers an introduction to Diophantine Geometry. The central theme is the investigation of the distribution of integral points on algebraic varieties. The text introduces problems in Diophantine Geometry, especially those involving integral points, assuming a geometrical perspective. It presents recent results not available in textbooks and also new viewpoints on classical material.