Congruences between modular forms and lowering the level mod ℓ n

Luis Dieulefait[1]; Xavier Taixés i Ventosa[2]

  • [1] Dept. d’Àlgebra i Geometria, Universitat de Barcelona Gran Via de les Corts Catalanes 585 08007 - Barcelona, Catalonia, Spain
  • [2] Institut für Experimentelle Mathematik, Universität Duisburg-Essen Ellernstraße 29 45326 Essen, Germany

Journal de Théorie des Nombres de Bordeaux (2009)

  • Volume: 21, Issue: 1, page 109-118
  • ISSN: 1246-7405

Abstract

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In this article we study the behavior of inertia groups for modular Galois mod ℓ n representations and in some cases we give a generalization of Ribet’s lowering the level result (cf. [9]).

How to cite

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Dieulefait, Luis, and Taixés i Ventosa, Xavier. "Congruences between modular forms and lowering the level mod $\ell ^n$." Journal de Théorie des Nombres de Bordeaux 21.1 (2009): 109-118. <http://eudml.org/doc/10864>.

@article{Dieulefait2009,
abstract = {In this article we study the behavior of inertia groups for modular Galois mod $\ell ^n$ representations and in some cases we give a generalization of Ribet’s lowering the level result (cf. [9]).},
affiliation = {Dept. d’Àlgebra i Geometria, Universitat de Barcelona Gran Via de les Corts Catalanes 585 08007 - Barcelona, Catalonia, Spain; Institut für Experimentelle Mathematik, Universität Duisburg-Essen Ellernstraße 29 45326 Essen, Germany},
author = {Dieulefait, Luis, Taixés i Ventosa, Xavier},
journal = {Journal de Théorie des Nombres de Bordeaux},
language = {eng},
number = {1},
pages = {109-118},
publisher = {Université Bordeaux 1},
title = {Congruences between modular forms and lowering the level mod $\ell ^n$},
url = {http://eudml.org/doc/10864},
volume = {21},
year = {2009},
}

TY - JOUR
AU - Dieulefait, Luis
AU - Taixés i Ventosa, Xavier
TI - Congruences between modular forms and lowering the level mod $\ell ^n$
JO - Journal de Théorie des Nombres de Bordeaux
PY - 2009
PB - Université Bordeaux 1
VL - 21
IS - 1
SP - 109
EP - 118
AB - In this article we study the behavior of inertia groups for modular Galois mod $\ell ^n$ representations and in some cases we give a generalization of Ribet’s lowering the level result (cf. [9]).
LA - eng
UR - http://eudml.org/doc/10864
ER -

References

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  1. Henri Carayol, Sur les Représentations Galoisiennes modulo ℓ attachées aux formes modulaires. Duke mathematical journal 59, 3 (1989), 785–801. Zbl0703.11027MR1046750
  2. Henri Darmon, Fred Diamond and Richard Taylor, Fermat’s Last Theorem. International Press, 1995. Zbl0877.11035MR1605752
  3. Ehud de Shalit, Hecke rings and universal deformation rings, in Modular Forms and Fermat’s Last Theorem. Springer, New York, 1997. Zbl1044.11578MR1638487
  4. Fred Diamond, An extension of Wiles’ results, in Modular Forms and Fermat’s Last Theorem. Springer, New York, 1997. Zbl0917.11021MR1638490
  5. Luis Dieulefait and Nuria Vila, Projective linear groups as Galois groups over ℚ via modular representations. J. Symbolic Comput. 30 (2000), 799–810. Zbl0999.12006MR1800679
  6. Wieb Bosma, John Cannon and Catherine Playoust, The Magma algebra system I: The user language. Journal of Symbolic Computation 24, 3-4 (1997), 235–265. Zbl0898.68039MR1484478
  7. Barry Mazur, An introduction to the deformation theory of Galois representations, in Modular Forms and Fermat’s Last Theorem. Tata Institute of Fundamental Research Studies in Mathematics, Springer, New York, 1997, 243–311. Zbl0901.11015MR1638481
  8. Kenneth A. Ribet, On ℓ -adic representations attached to modular forms II. Glasgow Math. J. 27 (1985), 185–194. Zbl0596.10027MR819838
  9. Kenneth A. Ribet, On Modular Representations of Gal ( Q ¯ / Q ) arising from modular forms. Invent. Math. 100 (1990), 431–476. Zbl0773.11039MR1047143
  10. Kenneth A. Ribet, Images of semistable Galois representations. Olga Taussky-Todd: in memoriam. Pacific J. Math. (1997), Special Issue, 277–297. Zbl0942.11032MR1610883
  11. Xavier Taixés i Ventosa, Theoretical and algorithmic aspects of congruences between modular Galois representations. Ph.D. Thesis, Institut für Experimentelle Mathematik (Universität Duisburg-Essen) (2009). Zbl1328.11059

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