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Fundamentals of Diophantine Geometry

Authors: Lang, S.

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About this Textbook

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.

Table of contents (13 chapters)

Buy this book

eBook $64.99
price for USA in USD (gross)
  • ISBN 978-1-4757-1810-2
  • Digitally watermarked, DRM-free
  • Included format: PDF
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Hardcover $109.99
price for USA in USD
  • ISBN 978-0-387-90837-3
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
Softcover $84.99
price for USA in USD
  • ISBN 978-1-4419-2818-4
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
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Bibliographic Information

Bibliographic Information
Book Title
Fundamentals of Diophantine Geometry
Authors
Copyright
1983
Publisher
Springer-Verlag New York
Copyright Holder
Springer Science+Business Media New York
eBook ISBN
978-1-4757-1810-2
DOI
10.1007/978-1-4757-1810-2
Hardcover ISBN
978-0-387-90837-3
Softcover ISBN
978-1-4419-2818-4
Edition Number
1
Number of Pages
XVIII, 370
Additional Information
Originally published by Wiley-Interscience
Topics