The search session has expired. Please query the service again.

The search session has expired. Please query the service again.

Residually reductible representations and modular forms

C.M. Skinner; Andrew J. Wiles

Publications Mathématiques de l'IHÉS (1999)

  • Volume: 89, page 5-126
  • ISSN: 0073-8301

How to cite

top

Skinner, C.M., and Wiles, Andrew J.. "Residually reductible representations and modular forms." Publications Mathématiques de l'IHÉS 89 (1999): 5-126. <http://eudml.org/doc/104160>.

@article{Skinner1999,
author = {Skinner, C.M., Wiles, Andrew J.},
journal = {Publications Mathématiques de l'IHÉS},
keywords = {modularity; two-dimensional Galois representations; universal deformation rings; Hecke rings},
language = {eng},
pages = {5-126},
publisher = {Institut des Hautes Études Scientifiques},
title = {Residually reductible representations and modular forms},
url = {http://eudml.org/doc/104160},
volume = {89},
year = {1999},
}

TY - JOUR
AU - Skinner, C.M.
AU - Wiles, Andrew J.
TI - Residually reductible representations and modular forms
JO - Publications Mathématiques de l'IHÉS
PY - 1999
PB - Institut des Hautes Études Scientifiques
VL - 89
SP - 5
EP - 126
LA - eng
KW - modularity; two-dimensional Galois representations; universal deformation rings; Hecke rings
UR - http://eudml.org/doc/104160
ER -

References

top
  1. [C] H. CARAYOL, Sur les représentations ℓ-adiques associées aux formes modulaires de Hilbert, Ann. Sci. Ec. Norm. Sup. IV, Ser. 19 (1986), 409-468. Zbl0616.10025MR89c:11083
  2. [Ca] P. CARTIER, La conjecture locale de Langlands pour GL(2) et la démonstration de Ph. Kutzko, in Bourbaki Seminar, Vol. 1979/1980, Lecture Notes in Math., 842, Springer, (1981), 112-138. Zbl0498.12013MR83c:12017
  3. [Ch] C.-L. CHAI, Arithmetic minimal compactification of the Hilbert-Blumenthal moduli spaces, Ann. of Math. (2) 131 (1990), no. 3, 541-554. Zbl0754.14030MR91i:11063
  4. [Co] J. COATES, p-adic L-functions and Iwasawa's theory, in Algebraic number fields : L-functions and Galois properties (Proc. Sympos., Univ. Durham, Durham, 1975), Academic Press (1977), 269-353. Zbl0393.12027MR57 #276
  5. [De] P. DELIGNE, Formes modulaires et représentations de GL(2), in Modular functions of one variable, II, Lecture Notes in Math., 349, Springer, (1973), 55-105. Zbl0271.10032MR50 #240
  6. [D-R] P. DELIGNE, K. RIBET, Values of abelian L-functions at negative integers over totally real fields, Invent. Math. 59 (1980), no. 3, 227-286. Zbl0434.12009MR81m:12019
  7. [DRS] B. DE SMIT, K. RUBIN, R. SCHOOF, Criteria for complete intersections, in Modular forms and Fermat's Last Theorem, Springer (1997), 343-356. Zbl0903.13003MR1638484
  8. [D1] F. DIAMOND, On deformation rings and Hecke rings, Ann. of Math. (2), 144 (1996), no. 1, 137-166. Zbl0867.11032MR97d:11172
  9. [D2] F. DIAMOND, The Taylor-Wiles construction and multiplicity one, Invent. Math. 128, (1997), no. 2, 379-391. Zbl0916.11037MR98c:11047
  10. [DT] F. DIAMOND, R. TAYLOR, Non optimal levels of mod ℓ modular representations, Invent. Math. 115 (1994), no. 3, 435-462. Zbl0847.11025MR95c:11060
  11. [FM] J.-M. FONTAINE, B. MAZUR, Geometric Galois representations, in Elliptic Curves, modular forms, and Fermat's Last Theorem (Hong Kong, 1993), Internat. Press (1995), 41-78. Zbl0839.14011MR96h:11049
  12. [Ge] S. GELBART, Automorphic Forms on Adele Groups, Annals of Math. Studies, Vol. 83, Princeton University Press (1975). Zbl0329.10018MR52 #280
  13. [GL] P. GÉRARDIN, J.-P. LABESSE, The solution of a base change problem for GL(2) (following Langlands, Saito, Shintani), in Automorphic forms, representations and L-functions, Proc. Symp. Pure Math., XXXIII, part 2, 115-133. Zbl0412.10018
  14. [G] A. GROTHENDIECK, Éléments de la géométrie algébrique IV, Étude locale des schémas et des morphismes de schémas (deuxième partie), Publ. Math. de l'IHES 24 (1965). Zbl0135.39701
  15. [H1] H. HIDA, On p-adic Hecke algebras for GL2 over totally real fields, Ann. of Math. (2) 128, (1988), no. 2, 295-384. Zbl0658.10034MR89m:11046
  16. [H2] H. HIDA, On nearly ordinary Hecke algebras for GL(2) over totally real fields, in Algebraic number theory, Adv. Stud. Pure Math., 17, Academic Press (1989) 139-169. Zbl0742.11026MR92f:11064
  17. [H3] H. HIDA, Nearly ordinary Hecke algebras and Galois representations of several variables, in Algebraic analysis, geometry, and number theory (Baltimore, MD 1988), John Hopkins Univ. Press (1989), 115-134. Zbl0782.11017MR2000e:11144
  18. [I] K. IWASAWA, On Zℓ extensions of algebraic number fields, Ann. of Math. (2) 98 (1973), 246-326. Zbl0285.12008MR50 #2120
  19. [J-L] H. JACQUET, R. LANGLANDS, Automorphic forms on GL(2), Lecture Notes in Math., 114, Springer (1970). Zbl0236.12010MR53 #5481
  20. [Ku] P. KUTZKO, The Langlands conjecture for GL2 of a local field, Ann. of Math. (2) 112, (1980), no. 2, 381-412. Zbl0469.22013
  21. [Mat] H. MATSUMURA, Commutative Ring Theory, Cambridge Studies in Advanced Mathematics, 8, Cambridge Univ. Press (1989). Zbl0666.13002MR90i:13001
  22. [M] B. MAZUR, Deforming Galois representations, in Galois Groups over Q, vol. 16, MSRI Publications, Springer (1989). Zbl0714.11076MR90k:11057
  23. [N] M. NAGATA, Local Rings, Interscience Tracts in Pure and Applied Mathematics, n° 13, Interscience Publishers (1962). Zbl0123.03402MR27 #5790
  24. [R] R. RAMAKRISHNA, On a variation of Mazur's deformation functor, Comp. Math. 87 (1993), 269-286. Zbl0910.11023MR94h:11054
  25. [Ray] M. RAYNAUD, Théorèmes de Lefschetz en cohomologie cohérent et en cohomologie étale, Bull. Soc. Math. France, Mém. no. 41. Supplément au Bull. Soc. Math. France, Tome 103, Société Mathématique de France (1975). Zbl0323.14007MR53 #10804
  26. [Ri] K. RIBET, Congruence relations between modular forms, Proc. Int. Cong. of Math. 17 (1983), 503-514. Zbl0575.10024MR87c:11045
  27. [Sch] M. SCHLESSINGER, Functors on Artin rings, Trans. AMS 130 (1968), 208-222. Zbl0167.49503MR36 #184
  28. [Se] J.-P. SERRE, Sur le résidu de la function zêta p-adique d'un corps de nombres, C.R. Acad. Sc. Paris 287, Serie A (1978), 183-188. Zbl0393.12026MR58 #22024
  29. [Shi] H. SHIMIZU, Theta series and modular forms on GL2, J. Math. Soc. Japan 24 (1973), 638-683. Zbl0241.10016MR48 #11406
  30. [Sh] G. SHIMURA, The special values of the zeta functions associated with Hilbert modular forms, Duke Math. J. 45 (1978), 637-679. Zbl0394.10015MR80a:10043
  31. [SW] C. SKINNER, A. WILES, Ordinary representations and modular forms, Proc. Nat. Acad. Sci. USA 94 (1997), no. 20, 10520-10527. Zbl0924.11044MR98h:11068
  32. [TW] R. TAYLOR, A. WILES, Ring-theoretic properties of certain Hecke algebras, Ann. of Math. (2), 141 (1995), no. 3, 553-572. Zbl0823.11030MR96d:11072
  33. [Wal] M. WALDSCHMIDT, A lower bound for the p-adic rank of the units of an algebraic number field, in Topics in classical number theory, Vol. I, II (Budapest, 1981), Colloq. Math. Soc. János Bolyai, 34, North-Holland (1984), 1617-1650. Zbl0541.12003MR86h:11095
  34. [Wa] L. WASHINGTON, The non-p-part of the class number in a cyclotomic Zp-extension, Invent. Math. 49 (1978), no. 1, 87-97. Zbl0403.12007MR80c:12005
  35. [We] A. WEIL, Basic Number Theory, Springer (1967). Zbl0176.33601MR38 #3244
  36. [W1] A. WILES, Modular elliptic curves and Fermat's Last Theorem, Ann. of Math. (2), 142 (1995), 443-551. Zbl0823.11029MR96d:11071
  37. [W2] A. WILES, On ordinary λ-adic representations associated to modular forms, Invent. Math. 94 (1988), 529-573. Zbl0664.10013MR89j:11051
  38. [W3] A. WILES, On p-adic representations for totally real fields, Ann. of Math. (2), 123 (1986), 407-456. Zbl0613.12013MR87g:11142

NotesEmbed ?

top

You must be logged in to post comments.

To embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.

Only the controls for the widget will be shown in your chosen language. Notes will be shown in their authored language.

Tells the widget how many notes to show per page. You can cycle through additional notes using the next and previous controls.

    
                

Note: Best practice suggests putting the JavaScript code just before the closing </body> tag.