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Synopsis
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.
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Fundamentals of Diophantine Geometry
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Soft cover. Condition: New. Dust Jacket Condition: New. International Edition. ***INTERNATIONAL EDITION*** Read carefully before purchase: This book is the international edition in mint condition with the different ISBN and book cover design, the major content is printed in full English as same as the original North American edition. The book printed in black and white, generally send in twenty-four hours after the order confirmed. All shipments contain tracking numbers. Great professional textbook selling experience and expedite shipping service. Seller Inventory # ABE-1614422073510
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Fundamentals of Diophantine Geometry Lang, S.
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Hardcover Aug 29, 1983. Condition: Used: Very Good. Fundamentals of Diophantine Geometry | S. Lang | Springer-Verlag, 1983, in-8 cartonnage éditeur, 369 pages. Solide couverture en bel état général. Intérieur bien frais. [BT1]. Seller Inventory # 0423UOUWHK5
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Fundamentals of Diophantine Geometry
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Fundamentals of Diophantine Geometry
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Fundamentals of Diophantine Geometry
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Springer New York Aug 1983, 1983
ISBN 10: 0387908374
ISBN 13: 9780387908373
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Buch. Condition: Neu. This item is printed on demand - it takes 3-4 days longer - Neuware -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. 392 pp. Englisch. Seller Inventory # 9780387908373
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Fundamentals of Diophantine Geometry
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Gebunden. Condition: New. Dieser Artikel ist ein Print on Demand Artikel und wird nach Ihrer Bestellung fuer Sie gedruckt. 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. Seller Inventory # 5911767
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Fundamentals of Diophantine Geometry
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Fundamentals of Diophantine Geometry
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