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On mod 3 Galois representations with conductor 4

Author: Hyunsuk Moon
Journal: Proc. Amer. Math. Soc. 135 (2007), 3109-3113
MSC (2000): Primary 11F80, 11S15
Published electronically: June 21, 2007
MathSciNet review: 2322740
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Abstract: The non-existence is proved of 2-dimensional mod 3 irreducible representations of $ \operatorname{Gal}(\overline{\mathbb{Q}}/\mathbb{Q})$ of Artin conductor dividing 4.

References [Enhancements On Off] (What's this?)

  • 1. L. E. Dickson, Linear Groups, Teubner, 1901, Leibzig.
  • 2. J. Jones, Tables of number fields with prescribed ramification, edu/~jj/.
  • 3. Chandrashekhar Khare, Serre’s modularity conjecture: the level one case, Duke Math. J. 134 (2006), no. 3, 557–589. MR 2254626, 10.1215/S0012-7094-06-13434-8
  • 4. Hyunsuk Moon, The non-existence of certain mod 𝑝 Galois representations, Bull. Korean Math. Soc. 40 (2003), no. 3, 537–544. MR 1996862, 10.4134/BKMS.2003.40.3.537
  • 5. Hyunsuk Moon and Yuichiro Taguchi, Refinement of Tate’s discriminant bound and non-existence theorems for mod 𝑝 Galois representations, Doc. Math. Extra Vol. (2003), 641–654 (electronic). Kazuya Kato’s fiftieth birthday. MR 2046611
  • 6. A. M. Odlyzko, Discriminant bounds, unpublished manuscript (1976), available at:
  • 7. Jean-Pierre Serre, Sur les représentations modulaires de degré 2 de 𝐺𝑎𝑙(\overline{𝑄}/𝑄), Duke Math. J. 54 (1987), no. 1, 179–230 (French). MR 885783, 10.1215/S0012-7094-87-05413-5
  • 8. J.-P. Serre, Local fields, Springer-Verlag, New York, 1979.
  • 9. D. A. Suprunenko, Matrix groups, American Mathematical Society, Providence, R.I., 1976. Translated from the Russian; Translation edited by K. A. Hirsch; Translations of Mathematical Monographs, Vol. 45. MR 0390025
  • 10. John Tate, The non-existence of certain Galois extensions of 𝑄 unramified outside 2, Arithmetic geometry (Tempe, AZ, 1993) Contemp. Math., vol. 174, Amer. Math. Soc., Providence, RI, 1994, pp. 153–156. MR 1299740, 10.1090/conm/174/01857

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Additional Information

Hyunsuk Moon
Affiliation: Department of Mathematics, College of Natural Sciences, Kyungpook National University, Daegu 702-701, Korea

Received by editor(s): March 2, 2006
Received by editor(s) in revised form: July 24, 2006
Published electronically: June 21, 2007
Communicated by: Ken Ono
Article copyright: © Copyright 2007 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.