Mod 2 and mod 5 icosahedral representations

Shepherd-Barron, N.; Taylor, R.

doi:10.1090/S0894-0347-97-00226-9

Mod 2 and mod 5 icosahedral representations

Authors: N. I. Shepherd-Barron and R. Taylor
Journal: J. Amer. Math. Soc. 10 (1997), 283-298
MSC (1991): Primary 11F41, 11G10, 14G05, 14G35
DOI: https://doi.org/10.1090/S0894-0347-97-00226-9
MathSciNet review: 1415322
Full-text PDF Free Access

J. H. Conway, R. T. Curtis, S. P. Norton, R. A. Parker, and R. A. Wilson, $\Bbb {ATLAS}$ of finite groups, Oxford University Press, Eynsham, 1985. Maximal subgroups and ordinary characters for simple groups; With computational assistance from J. G. Thackray. MR 827219
Avner Ash and Glenn Stevens, Modular forms in characteristic $l$ and special values of their $L$-functions, Duke Math. J. 53 (1986), no. 3, 849–868. MR 860675, DOI https://doi.org/10.1215/S0012-7094-86-05346-9

F. Diamond, On deformation rings and Hecke rings, Annals of Math. (2) 144 (1996), 137-166.

Igor Dolgachev and David Ortland, Point sets in projective spaces and theta functions, Astérisque 165 (1988), 210 pp. (1989) (English, with French summary). MR 1007155

P. Deligne and M. Rapoport, Correction to: “Les schémas de modules de courbes elliptiques” (Modular functions of one variable, II (Proc. Internat. Summer School, Univ. Antwerp, Antwerp, 1972), pp. 143–316, Lecture Notes in Math., Vol. 349, Springer, Berlin, 1973), Modular functions of one variable, IV (Proc. Internat. Summer School, Univ. Antwerp, Antwerp, 1972) Springer, Berlin, 1975, pp. p. 149. Lecture Notes in Math., Vol. 476 (French). MR 0382292

Alexander Grothendieck, Le groupe de Brauer. I. Algèbres d’Azumaya et interprétations diverses, Dix exposés sur la cohomologie des schémas, Adv. Stud. Pure Math., vol. 3, North-Holland, Amsterdam, 1968, pp. 46–66 (French). MR 244269

C.Hermite, Sur la résolution de l’équation du cinqième degré, Comptes Rendus 46 (1858).

F. Klein, Lectures on the icosahedron (transl. G.G. Morrice), Trübner, 1888.

Robert P. Langlands, Base change for ${\rm GL}(2)$, Annals of Mathematics Studies, No. 96, Princeton University Press, Princeton, N.J.; University of Tokyo Press, Tokyo, 1980. MR 574808

David Mumford, Tata lectures on theta. II, Progress in Mathematics, vol. 43, Birkhäuser Boston, Inc., Boston, MA, 1984. Jacobian theta functions and differential equations; With the collaboration of C. Musili, M. Nori, E. Previato, M. Stillman and H. Umemura. MR 742776

K. Rubin and A. Silverberg, Families of elliptic curves with constant mod $p$ representations, Elliptic curves, modular forms, & Fermat’s last theorem (Hong Kong, 1993) Ser. Number Theory, I, Int. Press, Cambridge, MA, 1995, pp. 148–161. MR 1363500

Jean-Pierre Serre, Œuvres. Vol. I, Springer-Verlag, Berlin, 1986 (French). 1949–1959. MR 926689

Jean-Pierre Serre, Sur les représentations modulaires de degré $2$ de ${\rm Gal}(\overline {\bf Q}/{\bf Q})$, Duke Math. J. 54 (1987), no. 1, 179–230 (French). MR 885783, DOI https://doi.org/10.1215/S0012-7094-87-05413-5

Jerrold Tunnell, Artin’s conjecture for representations of octahedral type, Bull. Amer. Math. Soc. (N.S.) 5 (1981), no. 2, 173–175. MR 621884, DOI https://doi.org/10.1090/S0273-0979-1981-14936-3

Richard Taylor and Andrew Wiles, Ring-theoretic properties of certain Hecke algebras, Ann. of Math. (2) 141 (1995), no. 3, 553–572. MR 1333036, DOI https://doi.org/10.2307/2118560

Gerard van der Geer, Hilbert modular surfaces, Ergebnisse der Mathematik und ihrer Grenzgebiete (3) [Results in Mathematics and Related Areas (3)], vol. 16, Springer-Verlag, Berlin, 1988. MR 930101

Andrew Wiles, Modular elliptic curves and Fermat’s last theorem, Ann. of Math. (2) 141 (1995), no. 3, 443–551. MR 1333035, DOI https://doi.org/10.2307/2118559