N. Bourbaki Éléments de mathématique. Chapitres 4 à 7, Masson, Paris 1981. Google Scholar

K. Buzzard, Analytic continuation of overconvergent eigenforms, J. Amer. Math. Soc. 16 (2003), no. 1, 29–55, (electronic). CrossrefGoogle Scholar

K. Buzzard, Computing weight 1 modular forms over $𝐂$ and ${\overline{𝐅}}_p$, preprint (2013), http://arxiv.org/abs/1205.5077.

K. Buzzard and R. Taylor, Companion forms and weight one forms, Ann. of Math. (2) 149 (1999), no. 3, 905–919. CrossrefGoogle Scholar

F. Calegari and D. Geraghty, Modularity lifting beyond the Taylor–Wiles method, preprint (2012), http://arxiv.org/abs/1207.4224.

R. F. Coleman and B. Edixhoven, On the semi-simplicity of the $U_p$-operator on modular forms, Math. Ann. 310 (1998), no. 1, 119–127. Google Scholar

H. Darmon, F. Diamond and R. Taylor, Fermat’s last theorem, Elliptic curves, modular forms & Fermat’s last theorem (Hong Kong 1993), International Press, Cambridge (1997), 2–140. Google Scholar

P. Deligne and M. Rapoport, Les schémas de modules de courbes elliptiques, Modular functions of one variable. II (Antwerp 1972), Lecture Notes in Math. 349, Springer, Berlin (1973), 143–316. Google Scholar

F. Diamond, The Taylor–Wiles construction and multiplicity one, Invent. Math. 128 (1997), no. 2, 379–391. CrossrefGoogle Scholar

B. Edixhoven, Comparison of integral structures on spaces of modular forms of weight two, and computation of spaces of forms mod 2 of weight one, J. Inst. Math. Jussieu 5 (2006), no. 1, 1–34. Google Scholar

T. Gee, Automorphic lifts of prescribed types, Math. Ann. 350 (2011), no. 1, 107–144. CrossrefWeb of ScienceGoogle Scholar

A. Grothendieck, Éléments de géométrie algébrique. IV. Étude locale des schémas et des morphismes de schémas. I, Publ. Math. Inst. Hautes Études Sci. 20 (1964), Paper No. 259. Google Scholar

N. M. Katz, p-adic properties of modular schemes and modular forms, Modular functions of one variable. III (Antwerp, 1972), Lecture Notes in Math. 350, Springer, Berlin (1973), 69–190. Google Scholar

N. M. Katz, A result on modular forms in characteristic p, Modular functions of one variable. V (Bonn 1976), Lecture Notes in Math. 601, Springer, Berlin (1977), 53–61. Google Scholar

C. Khare and J.-P. Wintenberger, Serre’s modularity conjecture. I, Invent. Math. 178 (2009), no. 3, 485–504. CrossrefGoogle Scholar

C. Khare and J.-P. Wintenberger, Serre’s modularity conjecture. II, Invent. Math. 178 (2009), no. 3, 505–586. CrossrefGoogle Scholar

M. Kisin, Moduli of finite flat group schemes, and modularity, Ann. of Math. (2) 170 (2009), no. 3, 1085–1180. CrossrefWeb of ScienceGoogle Scholar

M. Kisin, The Fontaine–Mazur conjecture for ${\mathrm{GL}}_2$, J. Amer. Math. Soc. 22 (2009), no. 3, 641–690. Google Scholar

B. Mazur, Modular curves and the Eisenstein ideal, Publ. Math. Inst. Hautes Études Sci. 47 (1977), 33–186. CrossrefGoogle Scholar

G. J. Schaeffer, Hecke stability and weight 1 modular forms, preprint (2014), http://arxiv.org/abs/1406.0408.

J. Shotton, Local deformation rings and a Breuil–Mézard conjecture when $l\ne p$, preprint (2013), http://arxiv.org/abs/1309.1600.

B. de Smit and H. W. Lenstra, Jr., Explicit construction of universal deformation rings, Modular forms and Fermat’s last theorem (Boston 1995), Springer, New York (1997), 313–326. Google Scholar

A. Snowden, Singularities of ordinary deformation rings, preprint (2011), http://arxiv.org/abs/1111.3654.

W. Stein, Modular forms, a computational approach, Grad. Stud. Math. 79, American Mathematical Society, Providence 2007. Google Scholar

R. Taylor, Automorphy for some l-adic lifts of automorphic mod l Galois representations. II, Publ. Math. Inst. Hautes Études Sci. 108 (2008), 183–239. CrossrefGoogle Scholar

R. Taylor and A. Wiles, Ring-theoretic properties of certain Hecke algebras, Ann. of Math. (2) 141 (1995), no. 3, 553–572. CrossrefGoogle Scholar

A. Wiles, Modular elliptic curves and Fermat’s last theorem, Ann. of Math. (2) 141 (1995), no. 3, 443–551. CrossrefGoogle Scholar