Author | Silverman, Joseph H. author |
---|---|

Title | Rational Points on Elliptic Curves [electronic resource] / by Joseph H. Silverman, John Tate |

Imprint | New York, NY : Springer New York : Imprint: Springer, 1992 |

Connect to | http://dx.doi.org/10.1007/978-1-4757-4252-7 |

Descript | X, 281 p. online resource |

SUMMARY

In 1961 the second author deliv1lred a series of lectures at Haverford Colยญ lege on the subject of "Rational Points on Cubic Curves. " These lectures, intended for junior and senior mathematics majors, were recorded, tranยญ scribed, and printed in mimeograph form. Since that time they have been widely distributed as photocopies of ever decreasing legibility, and porยญ tions have appeared in various textbooks (Husemoller [1], Chahal [1]), but they have never appeared in their entirety. In view of the recent interยญ est in the theory of elliptic curves for subjects ranging from cryptograยญ phy (Lenstra [1], Koblitz [2]) to physics (Luck-Moussa-Waldschmidt [1]), as well as the tremendous purely mathematical activity in this area, it seems a propitious time to publish an expanded version of those original notes suitable for presentation to an advanced undergraduate audience. We have attempted to maintain much of the informality of the origยญ inal Haverford lectures. Our main goal in doing this has been to write a textbook in a technically difficult field which is "readable" by the average undergraduate mathematics major. We hope we have succeeded in this goal. The most obvious drawback to such an approach is that we have not been entirely rigorous in all of our proofs. In particular, much of the foundational material on elliptic curves presented in Chapter I is meant to explain and convince, rather than to rigorously prove

CONTENT

I Geometry and Arithmetic -- II Points of Finite Order -- III The Group of Rational Points -- IV Cubic Curves over Finite Fields -- V Integer Points on Cubic Curves -- VI Complex Multiplication -- Appendix A Projective Geometry -- 1. Homogeneous Coordinates and the Projective Plane -- 2. Curves in the Projective Plane -- 3. Intersections of Projective Curves -- 4. Intersection Multiplicities and a Proof of Bezoutโ{128}{153}s Theorem -- Exercises -- List of Notation

Mathematics
Algebraic geometry
Mathematics
Algebraic Geometry