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| 內容簡介： |
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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.
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| 目錄：
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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
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