Elliptic Divisibility Sequences with Complex Multiplication

I Introduction 11 Elliptic divisibility sequences . . . . . . . . . . . . . . . . . . . . 12 Overview of the text . . . . . . . . . . . . . . . . . . . . . . . . . 23 Preview . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 34 Acknowledgements . . . . . . . . . . . . . . . . . . . . . . . . . . 5II Elliptic Curves 71 Elliptic curves . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 72 Invariant difierentials . . . . . . . . . . . . . . . . . . . . . . . . . 73 Elliptic curves over C . . . . . . . . . . . . . . . . . . . . . . . . 84 Complex multiplication . . . . . . . . . . . . . . . . . . . . . . . 9IIIThe Formal Group 111 Formal groups . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 121.1 Formal groups . . . . . . . . . . . . . . . . . . . . . . . . 121.2 The formal group of an elliptic curve . . . . . . . . . . . . 121.3 Groups associated to formal groups . . . . . . . . . . . . . 141.4 Difierentials and formal logarithms . . . . . . . . . . . . . 152 Elliptic curves over local flelds . . . . . . . . . . . . . . . . . . . . 162.1 Reduction modulo M . . . . . . . . . . . . . . . . . . . . 162.2 The formal group . . . . . . . . . . . . . . . . . . . . . . . 162.3 The groups