@MISC{Milne96ellipticcurves, author = {J. S. Milne}, title = {Elliptic Curves}, year = {1996} }

Share

OpenURL

Abstract

. These are the notes for Math 679, University of Michigan, Winter 1996, exactly as they were handed out during the course except for some minor corrections. Please send comments and corrections to me at jmilne@umich.edu using "Math679" as the subject. Contents Introduction 1 Fast factorization of integers Congruent numbers Fermat's last theorem 1. Review of Plane Curves 2 Affine plane curves Projective plane curves 2. Rational Points on Plane Curves. 6 Hensel's lemma A brief introduction to the p-adic numbers Some history 3. The Group Law on a Cubic Curve 12 4. Functions on Algebraic Curves and the Riemann-Roch Theorem 14 Regular functions on affine curves Regular functions on projective curves The Riemann-Roch theorem The group law revisited Perfect base fields 5. Definition of an Elliptic Curve 19 Plane projective cubic curves with a rational inflection point General plane projective curves Complete nonsingular curves of genus 1 Copyright 1996 J.S. Milne. You may make one...