The Arithmetic of Elliptic Curves
(Sprache: Englisch)
The theory of elliptic curves is distinguished by its long history and by the diversity of the methods that have been used in its study. This book treats the arithmetic theory of elliptic curves in its modern formulation, through the use of basic...
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Klappentext zu „The Arithmetic of Elliptic Curves “
The theory of elliptic curves is distinguished by its long history and by the diversity of the methods that have been used in its study. This book treats the arithmetic theory of elliptic curves in its modern formulation, through the use of basic algebraic number theory and algebraic geometry. The book begins with a brief discussion of the necessary algebro-geometric results, and proceeds with an exposition of the geometry of elliptic curves, the formal group of an elliptic curve, elliptic curves over finite fields, the complex numbers, local fields and global fields. The last two chapters deal with integral and rational points, including Siegel's theorem and explicit computations for the curve Y2=X3+DX. The book contains three appendices: Elliptic Curves in Characteristics 2 and 3, Group Cohomology, and a third appendix giving an overview of more advanced topics.
Inhaltsverzeichnis zu „The Arithmetic of Elliptic Curves “
Contents: Introduction.- Algebraic Varieties.- Algebraic Curves.- The Geometry of Elliptic Curves.- The Formal Group of Elliptic Curve.- Elliptic Curves over Finite Fields.- Elliptic Curves over C.- Elliptic Curves over Local Fields.- Elliptic Curves over Global Fields.- Integral Points on Elliptic Curves.- Computing the Mordell-Weil Group.- Appendix A: Elliptic Curves in Characteristics 2 and 3. - Appendix B: Group Cohomology (H0 and H1).- Appendix C.: Further Topics: An Overview.- Notes on Exercises.- Bibliography.- List of Notation.- Index.
Bibliographische Angaben
- Autor: Joseph H. Silverman
- XII, 400 Seiten, 13 Schwarz-Weiß-Abbildungen, Maße: 24,5 cm, Gebunden, Englisch
- Verlag: Springer, Berlin
- ISBN-10: 0387962034
- ISBN-13: 9780387962030
Sprache:
Englisch
Rezension zu „The Arithmetic of Elliptic Curves “
"This well-written book covers the basic facts about the geometry and arithmetic of elliptic curves, and is sure to become the standard reference in the subject. It meets the needs of at least three groups of people: students interested in doing research in Diophantine geometry, mathematicians needing a reference for standard facts about elliptic curves, and computer scientists interested in algorithms and needing an introduction to elliptic curves..."-- MATHEMATICAL REVIEWS
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