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On the Finiteness and Non-Existence of Certain Mod 2 Galois Representations of Quadratic Fields

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Some finiteness and non-existence results are proved of 2-dimensional mod 2 Galois representations of quadratic fields unramified outside 2.

Abstract

Some finiteness and non-existence results are proved of 2-dimensional mod 2 Galois representations of quadratic fields unramified outside 2.

참고문헌 (31)

  1. A. Ash, "Galois representations with conjectural connections to arithmetic cohomology", Duke Math. J, 112, pp.521~579 (2002)
  2. A. Ash, "An analogue of Serre's conjecture for Galois representations and Hecke eigenclasses in the mod p cohomology of GL(n,Z)", Duke Math. J, 105, pp.1~24 (2000)
  3. S. Brueggeman, "The nonexistence of certain Galois extensions unramified outside 5", J. Number Theory, 75, pp.47~52 (1999)
  4. S. Brueggeman, "The nonexistence of certain nonsolvable Galois extensions of number fields of small degree", Int. J. Number Theory, 1, pp.155~160 (2005)
  5. "On Serre's conjecrure for mod `Galois representations over totally real fields (http:", pp.bdj12.pdf), www.unet.brandeis.edu
  6. L. E. Dickson, "Linear Groups" (1901), Teubner
  7. B. Edixhoven, "The weight in Serre's conjectures on modular forms", Invent. Math, 109, pp.568~594 (1992)
  8. L. M. Figueiredo, "Serre's conjecture for imaginary quadratic fields", Compositio Math, 118, pp.103~122 (1999)
  9. "Tables of number fields with prescribed ramification"[URL]
  10. C. Khare, "Conjectures on finiteness of mod p Galois representations", J. Ramanujan Math. Soc, 15, pp.23~42 (2000)
  11. "Serre's modularity conjecture (http:", pp.papers.html), www.math.utah.edu
  12. H. Moon, "Finiteness results on certain mod p Galois representations", J. Number Theory, 84, pp.156~165 (2000)
  13. H. Moon, "The non-existence of certain mod p Galois representations", Bull. Korean Math. Soc, 40, pp.537~544 (2003)
  14. H. Moon, "On mod 3 Galois representations with conductor 4", Proc. Amer. Math. Soc, 통권 : 135, pp.3109~3113 (2007)
  15. H. Moon, "Mod p Galois representations of solvable image", Proc. Amer. Math. Soc, 129, pp.2529~2534 (2001)
  16. H. Moon, "Refinement of Tate's discriminant bound and non-existence theorems for mod p Galois representations", pp.641~654 (2003), Kazuya Kato's fiftieth birthday, Doc. Math. Extra Vol
  17. H. Moon, "The non-existence of certain mod 2 Galois representations of some small quadratic fields", Proc. Japan Acad, 84, pp.57~61 (2008)
  18. A. Odlyzko, "Lower bounds for discriminants of number fields. II", TÔhoku Math. J, 29, pp.209~216 (1977)
  19. "Discriminant bounds, unpublished manuscript"[URL]
  20. K. Ono, "2-adic properties of certain modular forms and their applications to arithmetic functions", Int. J. Number Theory, 1, pp.75~101 (2005)
  21. G. Poitou, "Minorations de discriminants (d’apr`es A. M. Odlyzko)", pp.136~153 (1977), Lecture Notes in Math, Springer, Berlin
  22. "Weights in Serre's conjecture for Hilbert modular forms"[URL]
  23. M.H.Sengün, "The non-existence of certain representations of the absolute Galois group of quadratic fields" (2007), preprint
  24. J.-P. Serre, "Valeurs propres des op´erateurs de Hecke modulo ℓ, Journées Arithmé tiques de Bordeaux", pp.109~117 (1974), Astérisque 24-25, Soc. Math. France, Paris
  25. J.-P. Serre, "Minorations de discriminants, OEuvres III", pp.240~243 (1986), Springer-Verlag
  26. J.-P. Serre, "Note 229.2, OEuvres III", pp.710~ (1986), Springer-Verlag
  27. J.-P. Serre, "Sur les repré sentations modulaires de degré 2 de Gal(Q", Q), 1987, pp.54, 179~230
  28. D. A. Suprunenko, "Matrix Groups" (1976), Amer. Math. Soc., Providence
  29. T. Takagi, "Algebraic Number Theory, 2nd ed. (in Japanese)" (1971), Iwanami Shoten, Tokyo
  30. J. Tate, "The non-existence of certain Galois extensions of Q unramified outside 2, in: "Arithmetic Geometry"", pp.153~156 (1994), Contemp. Math., 174, Amer. Math. Soc., Providence, RI
  31. A. Weil, "Sur les “formules explicites” de la thé orie des nombres premiers", pp.252~265 (1952), Comm. Sém. Math. Univ. Lund, Tome Supplementaire

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