From the Taniyama-Shimura conjecture to Fermat's last theorem

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1. [1] Atkin ( A.O.L.) and Lehner ( J.) .— Hecke operators on Γo(m), Math. Ann.185, 134-160 (1970) Zbl0177.34901MR268123
2. [2] Carayol ( H.) .— Sur la mauvaise réduction des courbes de Shimura, Compositio Math.59, 151-230 (1986) Zbl0607.14021MR860139
3. [3] Cerednik ( I.V.) .— Uniformization of algebraic curves by discrete arithmetic subgroups of PGL2(kw) with compact quotients (in Russian), Mat. Sb.100 , 59-88 (1976). Translation in Math USSR Sb.29, 55-78 (1976) Zbl0379.14010MR491706
4. [4] Deligne ( P.) and Rapoport ( M.) .— Les schémas de modules de courbes elliptiques, Lecture Notes in Math.349, 143-316 (1973) Zbl0281.14010MR337993
5. [5] Deligne ( P.) AND Serre ( J-P.) .— Formes modulaires de poids 1, Ann. Sci. Ec. Norm. Sup.7, 507-530 (1974) Zbl0321.10026MR379379
6. [6] Drinfeld ( V.G.) .— Coverings of p-adic symmetric regions (in Russian), Functional. Anal. i Prilozen.10, 29-40 (1976). Translation in Funct. Anal. Appl.10, 107-115 (1976) Zbl0346.14010MR422290
7. [7] Edixhoven ( S.J.) .— Minimal resolution and stable reduction of Xo(N), To appear Zbl0679.14009
8. [8] Edixhoven ( S.J.) .— L'action de l'algèbre de Hecke sur les groupes de composantes des jacobiennes des courbes modulaires est "Eisenstein", To appear Zbl0781.14019MR1141457
9. [9] Faltings ( G.) .— Endlichkeitssätze für abelsche Varietäten über Zahlkörpern, Invent. Math73, 349-366 (1983). English translation in : Arithmetic Geometry, G. Cornell and J. H. Silverman, eds. New York : Springer-Verlag (1986) Zbl0588.14026MR718935
10. [10] Frey ( G.) .— Links between stable elliptic curves and certain diophantine equations, Annales Universitatis Saraviensis1, 1-40 (1986) Zbl0586.10010MR853387
11. [11] Frey ( G.) .— Links between solutions of A - B = C and elliptic curves, Lecture Notes in Math.1380, 31-62 (1989) Zbl0688.14018MR1009792
12. [12] Grothendieck ( A.) .— SGA7 I, Exposé IX. Lecture Notes in Math.288, 313-523 (1972) Zbl0248.14006
13. [13] Husemöller ( D.) .— Elliptic Curves, Graduate Texts in Mathematics111. New York: Springer-Verlag (1987) Zbl0605.14032MR868861
14. [14] Jordan ( B.) and Livné ( R.) .— Local diophantine properties of Shimura curves, Math. Ann.270, 235-248 (1985) Zbl0536.14018MR771981
15. [15] Jordan ( B.) and Livné ( R.) .— On the Néron model of Jacobians of Shimura curves, Compositio Math.60, 227-236 (1986) Zbl0609.14018MR868139
16. [16] Katz ( N.M.) and Mazur ( B.) .— Arithmetic Moduli of Elliptic Curves, Annals of Math. Studies108. Princeton: Princeton University Press, (1985) Zbl0576.14026MR772569
17. [17] Kurihara ( A.) . — On some examples of equations defining Shimura curves and the Mumford uniformization, J. Fac. Sci. Univ. Tokyo, Sec. IA, 25, 277-300 (1979) Zbl0428.14012MR523989
18. [18] Mazur ( B.) .— Modular curves and the Eisenstein ideal, Publ. Math. IHES47, 33-186 (1977) Zbl0394.14008MR488287
19. [19] Mazur ( B.) .— Number theory as gadfly, American Math. Monthly. To appear Zbl0764.11021MR1121312
20. [20] Mazur ( B.) AND Ribet ( K.) .— Two-dimensional representations in the arithmetic of modular curves, To appear Zbl0780.14015MR1141460
21. [21] Oesterlé ( J.) .— Nouvelles approches du "théorème" de Fermat, Séminaire Bourbaki n° 694 (1987-88). Astérisque161-162, 165-186 (1988) Zbl0668.10024MR992208
22. [22] Ogg ( A.) .— Rational points on certain elliptic modular curves, Proc. Symp. Pure Math.24, 221-231 (1973) Zbl0273.14008MR337974
23. [23] Ogg ( A.).— Hyperelliptic modular curves, Bull. SMF102, 449-462 (1974) Zbl0314.10018MR364259
24. [24] Raynaud ( M.) .— Spécialisation du foncteur de Picard, Publ. Math. IHES38, 27-76 (1970) Zbl0207.51602MR282993
25. [25] Ribet ( K.) .— On modular representations of Gal(Q/Q) arising from modular forms, Preprint Zbl0773.11039MR1047143
26. [26] Ribet ( K.) .— Bimodules and abelian surfaces, Advanced Studies in Pure Mathematics17, 359-407 (1989) Zbl0742.11033MR1097624
27. [27] Ribet ( K.) .— On the component groups and the Shimura subgroup of Jo(N), Sém. Th. Nombres, Université Bordeaux, 1987-88 Zbl0691.14009MR993107
28. [28] Serre ( J-P.) .— Abelian l-adic Representations and Elliptic Curves, New York: W.A. Benjamin1968. (Republished 1989 by Addison-Wesley) Zbl0186.25701
29. [29] Serre ( J-P.) .— Propriétés galoisiennes des points d'ordre fini des courbes elliptiques, Invent. Math.15, 259-331 (1972) Zbl0235.14012MR387283
30. [30] Serre ( J-P.) .— Sur les représentations modulaires de degré 2 de Gal(Q/Q), Duke Math. J.54, 179-230 (1987) Zbl0641.10026MR885783
31. [31] Serre ( J-P.) and Tate, ( J.) .— Good reduction of abelian varieties, Ann. of Math.88, 492-517 (1968) Zbl0172.46101MR236190
32. [32] Shimura ( G.) .— Introduction to the Arithmetic Theory of Automorphic Functions, Princeton: Princeton University Press (1971) Zbl0221.10029
33. [33] Shimura ( G.) . — On elliptic curves with complex multiplication as factors of the Jacobians of modular function fields, Nagoya Math. J.43, 199-208 (1971) Zbl0225.14015MR296050
34. [34] Silverman ( J.) .— The Arithmetic of Elliptic Curves, Graduate Texts in Mathematics106. New York: Springer-Verlag (1986) Zbl0585.14026MR817210
35. [35] Weil ( A.) .— Über die Bestimmung Dirichletscher Reihen durch Funktionalgleichungen, Math. Ann.168, 165- 172 (1967) Zbl0158.08601MR207658

1. Kenneth A. Ribet, Wiles dokázal Taniyamovu hypotézu; důsledkem je Fermatova věta
2. Jan Nekovář, Modulární křivky a Fermatova věta