TY - BOOK ID - 18113007 TI - The arithmetic of elliptic curves PY - 1986 VL - 106 SN - 0387962034 3540962034 1475719221 1475719205 9780387962030 PB - New York, NY : Springer-Verlag, DB - UniCat KW - Arithmetic. KW - Curves, Algebraic. KW - Curves, Elliptic. KW - Curves, Elliptic KW - Curves, Algebraic KW - Courbes algébriques KW - 512.74 KW - Elliptic curves KW - Numbers, Real KW - Algebraic groups. Abelian varieties KW - 512.74 Algebraic groups. Abelian varieties KW - Courbes algébriques KW - Arithmetic KW - Algebraic curves KW - Algebraic varieties KW - Mathematics KW - Set theory KW - Calculators KW - Algebraic geometry KW - Courbes elliptiques KW - Arithmétique KW - Arithmetical algebraic geometry KW - Géométrie algébrique arithmétique KW - Géométrie algébrique KW - Géométrie algébrique arithmétique. KW - Géométrie algébrique KW - Nombres, Théorie des UR - https://www.unicat.be/uniCat?func=search&query=sysid:18113007 AB - 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 Y 2 = X 3 + 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. ER -