Search results with tag "Elliptic curves"
THE RISING SEA Foundations of Algebraic Geometry
math.stanford.edu19.8. Curves of genus 4and 5 521 19.9. Curves of genus 1 523 19.10. Elliptic curves are group varieties 532 19.11. Counterexamples and pathologies using elliptic curves 538 Chapter 20. Application: A glimpse of intersection theory 543 20.1. Intersecting nline bundles with an n-dimensional variety 543 20.2. Intersection theory on a surface 547 20.3.
J.S. Milne: Elliptic Curves
www.jmilne.orgPreface In early 1996, I taught a course on elliptic curves. Since this was not long after Wiles hadprovedFermat’sLast TheoremandI promisedto explainsome ofthe
Introduction to Algebraic Geometry
www.five-dimensions.orgCurves 305 6.1. Basic properties 305 6.2. Elliptic curves 313 6.3. The Riemann-Roch Theorem 323 6.4. The modern approach to Riemann-Roch 331 6.5. The Hurwitz-Riemann Formula 333 6.6. The j-invariant 337 Appendix A. Algebra 341 A.1. Rings 341 A.2. Fields 386 A.3. Unique factorization domains 411 A.4. Further topics in ring theory 419 A.5. A ...
Introduction to arithmetic geometry
math.mit.edu41. Height functions on elliptic curves 67 42. Descent 70 43. Faltings’ theorem 71 Acknowledgements 71 References 71 1. What is arithmetic geometry? Algebraic geometry studies the set of solutions of a multivariable polynomial equation (or a system of such equations), usually over R or C. For instance, x2 + xy 5y2 = 1 de nes a hyperbola.