Introduction to arithmetic geometry
41. 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.
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