Reference: | [1] M. F. Atiyah and I. G. Macdonald, Introduction to Commutative Algebra, Addison-Wesley Publishing Co., Reading, Mass.-London-Don Mills, Ont., 1969. [2] C. Breuil, B. Conrad, F. Diamond, and R. Taylor, On the modularity of elliptic curves over Q: wild 3-adic exercises, J. Amer. Math. Soc. 14 (2001), no. 4, 843–939. [3] J. W. S. Cassels and A. Fro ̈hlich (eds.), Algebraic Number Theory (2nd edition), London, United Kingdom, London Mathematical Society, 2010, Reprint of the 1967 original. MR 911121 (88h:11073) [4] L. Clozel, M. Harris, and R. Taylor, Automorphy for some l-adic lifts of automorphic mod l Galois representations, Publ. Math. Inst. Hautes E ́tudes Sci. (2008), no. 108, 1–181, With Appendix A, summarizing unpublished work of Russ Mann, and Appendix B by Marie-France Vigne ́ras. [5] B. Conrad, F. Diamond, and R. Taylor, Modularity of certain potentially Barsotti-Tate Galois representations, J. Amer. Math. Soc. 12 (1999), no. 3, 521–567. [6] B. de Smit and H. W. Lenstra, Jr. , Explicit construction of universal deformation rings, Modular forms and Fermat’s last theorem (Boston, MA, 1995), Springer, 1997, pp. 313–326. [7] F. Diamond, On deformation rings and Hecke rings, Ann. of Math. (2) 144 (1996), no. 1, 137–166. [8] J.-M. Fontaine and B. Mazur, Geometric Galois representations, Elliptic curves, modular forms, & Fermat’s last theorem (Hong Kong, 1993), Ser. Number Theory, I, Int. Press, Cambridge, MA, 1995, pp. 41–78. [9] A. Grothendieck, Technique de descente et th ́eor"emes d’existence en g ́eom ́etrie alg ́ebrique. II. Le th ́eor"eme d’existence en th ́eorie formelle des modules, Se ́minaire Bourbaki, vol. 5, Socie ́te ́ Mathe ́matique de France, 1995, pp. 369–390. [10] A. Grothendieck and J. Dieudonne ́, El ́ements de G ́eom ́etrie Alg ́ebrique, Publ. Math. IHES,4 (1960), 8 (1961), 11 (1961), 17 (1963), 20 (1964), 24 (1965), 28 (1966), 32 (1967). [11] K. Haberlan, Galois Cohomology of Algebraic Number Fields, VEB Deutscher Verlag der Wissenschaften, Berlin, 1978, With two appendices by Helmut Koch and Thomas Zink. [12] M. Harris, N.Shepherd-Barron, and R. Taylor, A family of Calabi-Yau varieties and potential automorphy, Ann. of Math. (2) 171 (2010), no. 2, 779–813. [13] H. Hida, Galois representations into GL_2(Z_p[X]) attached to ordinary cusp forms, Invent. Math. 85 (1986), no. 3, 545–613. [14] C. Khare and J.-P. Wintenberger, Serre’s modularity conjecture. I, Invent. Math. 178 (2009), no. 3, 485–504. [15] C. Khare and J.-P. Wintenberger, Serre’s modularity conjecture. II, Invent. Math. 178 (2009), no. 3, 505–586. [16] M. Kisin, The Fontaine-Mazur conjecture for GL_2, J. Amer. Math. Soc. 22 (2009), no. 3, 641–690. [17] M. Kisin, Lecture Notes on Deformations of Galois Representations, Clay Mathematics Institute 2009 Summer School on Galois Representations (University of Hawaii at Manoa, Honolulu, Hawaii), June 15 - July 10 2009. [18] M. Kisin, Moduli of finite flat group schemes and modularity, Ann. of Math. (2) 170 (2009), no. 3, 1085–1180. [19] S. Mac Lane, Categories for the working mathematician, 2nd ed., Graduate Texts in Mathematics, vol. 5, Springer-Verlag, 1998. [20] B. Mazur, Deforming of Galois Representations, Galois Groups over Q (Y. Ihara, K. Ribet, and J.-P. Serre, eds.), Mathematical Sciences Research Institute Publications, no. 16, Springer-Verlag, 1987, pp. 385–437. [21] B. Mazur, An introduction to the deformation theory of Galois representations, Modular forms and Fermat’s last theorem (Boston, MA, 1995), Springer-Verlag, New York, 1997, pp. 243–311. [22] J. Neukirch, Algebraic Number Theory, Grundlehren der mathematischen Wissenschaften, vol. 322, Springer-Verlag, 1999. [23] R. Ramakrishna, On a variation of Mazur’s deformation functor, Compositio Math. 87 (1993), 269–286. [24] M. Schlessinger, Functors of Artin rings, Trans. A.M.S. 130 (1968), 208–222. [25] J.-P. Serre, Local fields, Graduate Texts in Mathematics, vol. 67, Springer-Verlag, 1979. [26] J.-P. Serre, Linear representations of finite groups, Graduate Texts in Mathematics, vol. 42, Springer-Verlag, New York, 1996. [27] J.-P. Serre, Galois cohomology, Springer Monographs in Mathematics, Springer-Verlag, 1997. [28] R. Taylor, Automorphy for some l-adic lifts of automorphic mod l Galois representations. II, Publ. Math. Inst. Hautes E ́tudes Sci. (208), no. 108, 183–239. [29] R. Taylor and A. Wiles, Ring-theoretic properties of certain Hecke algebras, Ann. of Math. 141 (1995), no. 3, 553–572. [30] J. Tilouine, Deformations of Galois representations and Hecke algebras, Published for The Mehta Research Institute of Mathematics and Mathematical Physics, Allahabad, 1996. [31] A. Wiles, Modular elliptic curves and Fermat’s Last Theorem, Ann. of Math. 141(1995), no.3, 443–551. |