Fundamentals Of Diophantine Geometry PDF Download
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Author | : S. Lang |
Publisher | : Springer Science & Business Media |
Total Pages | : 383 |
Release | : 2013-06-29 |
Genre | : Mathematics |
ISBN | : 1475718101 |
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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 | : Serge Lang |
Publisher | : |
Total Pages | : 370 |
Release | : 1983-01-01 |
Genre | : Arithmetical algebraic geometry |
ISBN | : 9783540908371 |
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Author | : Serge Lang |
Publisher | : Springer Science & Business Media |
Total Pages | : 68 |
Release | : 1997-04-14 |
Genre | : Mathematics |
ISBN | : 9783540612230 |
Download Number Theory III Book in PDF, ePub and Kindle
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.
Author | : Serge Lang |
Publisher | : |
Total Pages | : 192 |
Release | : 1962 |
Genre | : Diophantine analysis |
ISBN | : |
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Author | : Serge Lang |
Publisher | : Springer Science & Business Media |
Total Pages | : 553 |
Release | : 2012-12-06 |
Genre | : Mathematics |
ISBN | : 1461205417 |
Download Fundamentals of Differential Geometry Book in PDF, ePub and Kindle
This book provides an introduction to the basic concepts in differential topology, differential geometry, and differential equations, and some of the main basic theorems in all three areas. This new edition includes new chapters, sections, examples, and exercises. From the reviews: "There are many books on the fundamentals of differential geometry, but this one is quite exceptional; this is not surprising for those who know Serge Lang's books." --EMS NEWSLETTER
Author | : Umberto Zannier |
Publisher | : Springer |
Total Pages | : 420 |
Release | : 2007-06-27 |
Genre | : Mathematics |
ISBN | : |
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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.
Author | : Marc Hindry |
Publisher | : Springer Science & Business Media |
Total Pages | : 574 |
Release | : 2013-12-01 |
Genre | : Mathematics |
ISBN | : 1461212103 |
Download Diophantine Geometry Book in PDF, ePub and Kindle
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 | : Cambridge University Press |
Total Pages | : 73 |
Release | : 2007-09-06 |
Genre | : Mathematics |
ISBN | : 1139447955 |
Download Heights in Diophantine Geometry Book in PDF, ePub and Kindle
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 | : Serge Lang |
Publisher | : Hassell Street Press |
Total Pages | : 0 |
Release | : 2021-09-09 |
Genre | : Mathematics |
ISBN | : 9781013889110 |
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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.
Author | : N.B. Singh |
Publisher | : N.B. Singh |
Total Pages | : 63 |
Release | : |
Genre | : Mathematics |
ISBN | : |
Download Diophantine Discoveries Fundamentals Book in PDF, ePub and Kindle
"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.