Modular elliptic curves and Fermat’s last theorem

Introduction......Page 1 Table of Contents......Page 12 1.1 Deformations of Galois representations......Page 13 1.2 Some computations of cohomology groups......Page 30 1.3 Some results on subgroups of GL2(k)......Page 33 2.1 The Gorenstein property......Page 38 2.2 Congruences between Hecke rings......Page 47 2.3 The main conjectures......Page 61 3 Estimates for the Selmer group......Page 75 4.1 The ordinary CM case......Page 83 4.2 Calculation of η......Page 91 5 Application to elliptic curves......Page 99 Appendix Gorenstein rings and local complete intersections......Page 103 References......Page 106