Rational points on elliptic curves by John Tate, Joseph H. Silverman

Rational points on elliptic curves



Rational points on elliptic curves book




Rational points on elliptic curves John Tate, Joseph H. Silverman ebook
Format: djvu
Page: 296
ISBN: 3540978259, 9783540978251
Publisher: Springer-Verlag Berlin and Heidelberg GmbH & Co. K


If time permits, additional topics may be covered. You ask for an easy example of a genus 1 curve with no rational points. The subtitle is: Curves, Counting, and Number Theory and it is an introduction to the theory of Elliptic curves taking you from an introduction up to the statement of the Birch and Swinnerton-Dyer (BSD) Conjecture. Similarly, if P is constrained to lie on one of the sides of the square, it becomes equivalent to showing that there are no non-trivial rational points on the elliptic curve y^2 = x^3 - 7x - 6 . Rational functions and rational maps; Quasiprojective varieties. Consider the plane curve Ax^2+By^4+C=0. One reason for interest in the BSD conjecture is that the Clay Mathematics Institute is of a rational parametrization which is introduced on page 10. That is, an equation for a curve that provides all of the rational points on that curve. The genus 1 — elliptic curve — case will be in the next posting, or so I hope.) If you are interested in curves over fields that are not B, I want to mention the fact that there is no number N such that every genus 1 curve over a field k has a point of degree at most N over k. Rational curves; Relation with field theory; Rational maps; Singular and nonsingular points; Projective spaces. Affine space and the Zariski topology; Regular functions; Regular maps. Two days ago Benji Fisher came to my workshop to talk about group laws on rational points of weird things in the plane. The Zariski topology on Additional topics. Possibilities include the 27 lines on a cubic surface, or an introduction to elliptic curves. Degenerate Elliptic Curves in the plane.