內容介紹 | |
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出版社:世界圖書出版公司
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ISBN:9787510070174
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作者:(美)康奈爾
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頁數:582
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出版日期:2014-03-01
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印刷日期:2014-03-01
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包裝:平裝
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開本:24開
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版次:1
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印次:1
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康奈爾編著的《模形式與費馬大定理》內容介紹 :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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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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