模形式与费马大定理

　　康奈尔编著的《模形式与费马大定理》内容介绍 ：This volume is the record of an instructional conference on number theory and arithmetic 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 “behind-the-scenes” folks whose assistance was indispensable in running the con-ference. 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.

preface
contributors
schedule of lectures
introduction
chapter Ⅰ
　an overview of the proof of fermat’s last theorem
glenn stevens
　1. a remarkable elliptic curve
　2. galois representations
　3. a remarkable galois representation
　4. modular galois representations
　5. the modularity conjecture and wiles’s theorem
　6. the proof of fermat’s last theorem
　7. the proof of wiles’s theorem
　references
chapter Ⅱ
　a survey of the arithmetic theory of elliptic curves
　joseph h. silverman
　1. basic definitions
　2. the group law
　3. singular cubics
　4. isogenies
　5. the endomorphism ring
　6. torsion points
　7. galois representations attached to e
　8. the well pairing
　9. elliptic curves over finite fields
　10. elliptic curves over c and elliptic functions
　11. the formal group of an elliptic curve
　12. elliptic curves over local fields
　13. the selmer and shafarevich-tate groups
　14. discriminants, conductors, and l-series
　15. duality theory
　16. rational torsion and the image of galois
　17. tate curves
　18. heights and descent
　19. the conjecture of birch and swinnerton-dyer
　20. complex multiplication
　21. integral points
　references
chapter Ⅲ
　modular curves, hecke correspondences, and l-functions
　david e. rohrlich
chapter Ⅳ
　galois cohomology
　lawrence c. washington
chapter Ⅴ
　finite flat group schemes
　john tate
chapter Ⅵ
　three lectures on the modularity of pr,3 and the langlands reciprocity conjecture
　stephen gelhart
chapter Ⅶ
　serre’s conjectures
　bas edixhoven
chapter Ⅷ
　an introduction to the deformation theory of galois representations
　barry mazur
chapter Ⅸ
　explicit construction of universal deformation rings
　bart de smit and hendrik w. lenstra, jr.
chapter Ⅹ
　hecke algebras and the gorenstein property
　acques tilouine
chapter Ⅺ
　criteria for complete intersections
　bart de smit, karl rubin, and rene schoof
chapter Ⅻ
　l-adic modular deformations and wiles’s “main conjecture”
　fred diamond and kenneth a. ribet
chapter ⅫⅠ
　the flat deformation functor
　brian conrad
chapter ⅩⅣ
　hecke rings and universal deformation rings
　ehud de shalit
chapter ⅩⅤ
　explicit families of elliptic curves
　with prescribed mod n representations
　alice silverberg
chapter ⅩⅥ
　modularity of mod 5 representations
　karl rubin
chapter ⅩⅦ
　an extension of wiles’ results
　fred diamond
　appendix to chapter ⅩⅦ
　classification of ρe,l by the j invariant of e
　fred diamond and kenneth kramer
chapter ⅩⅧ
　class field theory and the first case of fermat’s last theorem
　hendrik w. lenstra, jr. and peter stevenhagen
chapter ⅪⅩ
　remarks on the history of fermat’s last theorem 1844 to 1984
　michael rosen
　introduction
　appendix a: kummer congruence and hilbert’s theorem
　bibliography