This volume is the record of an instructional conference on number theory and arithme …… [ 展开全部 ]
tic geometry held from August 9 through 18， 1995 at Boston University. It contains expanded versions of all of the major lectures given during the conference. We want to thank all of the speakers， all of the writers whose contributions make up this volume， and all of the "behindthe-scenes" folks whose assistance was indispensable in running the conference. We would especially like to express our appreciation to Patricia Pacelli， who coordinated most of the details of the conference while in the midst of writing her PhD thesis， to Jaap Top and Jerry Tunnell， who stepped into the breach on short notice when two of the invited speakers were unavoidably unable to attend， and to Stephen Gelbart， whose courage and enthusiasm in the face of adversity has been an inspiration to us. [ 收起 ]
Preface
Contributors
Schedule of Lectures
Introduction
CHAPTER Ⅰ
An Overview of the Proof of Fermat's Last Theorem
A remarkable elliptic curve
Galois representations
A remarkable Galois representation
Modular Galois representations
The Modularity Conjecture and Wiles's Theorem
The proof of Fermat's Last Theorem
The proof of Wiles's Theorem
References
CHAPTER Ⅱ
A Survey of the Arithmetic Theory of Elliptic Curv
Basic definitions
The group law
Singular cubics
Isogenies
The endomorphism ring
Torsion points
Galois representations attached to E
The Weil pairing
Elliptic curves over finite fields
Elliptic curves over C and elliptic functions
The formal group of an elliptic curve
Elliptic curves over local fields
The Selmer and Shafarevich-Tate groups
Discriminants, conductors, and L-series
Duality theory
Rational torsion and the image of Galois
Tate curves
Heights and descent
The conjecture of Birch and Swinnerton-Dyer
Complex multiplication
Integral points
References
CHAPTER Ⅲ
Modular Curvcs, Hecke Correspondences, and L-Funct
Modular curves
The Hcckc corrospondences
L-functions
Rcfcrcnccs
CHAPTER Ⅳ