ISBN: 3-540-66546-3
TITLE: Arithmetic Theory of Elliptic Curves
AUTHOR: Coates, J.; Greenberg, R.; Ribet, K.A.; Rubin, K.
TOC:
Fragments of the GL_2 Iwasawa Theory of Elliptic Curves without Complex Multiplication
John Coates 1
1 Statement of results 2
2 Basic properties of the Selmer group 14
3 Local cohomology calculations 23
4 Global calculations 39
Iwasawa Theory for Elliptic Curves
Ralph Greenberg 51
1 Introduction 51
2 Kummer theory for E 62
3 Control theorems 72
4 Calculation of an Euler characteristic 85
5 Conclusion 105
Torsion Points on J_0(N)and Galois Representations
Kenneth A. Ribet 145
1 Introduction 145
2 A local study at N 148
3 The kernel of the Eisenstein ideal 151
4 Lenstra's input 154
5 Proof of Theorem 1.7 156
6 Adelic representations 157
7 Proof of Theorem 1.6 163
Elliptic Curves with Complex Multiplication and the Conjecture of Birch and Swinnerton-Dyer
Karl Rubin 167
1 Quick review of elliptic curves 168
2 Elliptic curves over C 170
3 Elliptic curves over local fields 172
4 Elliptic curves over number fields 178
5 Elliptic curves with complex multiplication 181
6 Descent 188
7 Elliptic units 193
8 Euler systems 203
9 Bounding ideal class groups 209
10 The theorem of Coates and Wiles 213
11 Iwasawa theory and the "main conjecture" 216
12 Computing the Selmer group 227
END