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ON FOUR-DIMENSIONAL MOD 2 GALOIS REPRESENTATIONS AND A CONJECTURE OF ASH ET AL

  • Moon, Hyun-Suk (Department of Mathematics College of Natural Sciences Kyungpook National University)
  • Published : 2007.02.28

Abstract

The non-existence is proved of four-dimensional mod 2 semisimple representations of Gal ($\=\mathbb{Q}/\mathbb{Q}$) which are unramified outside 2.

Keywords

References

  1. A. Ash, D. Doud, and D. Pollack, Galois representations with conjectural connections to arithmetic cohomology, Duke Math. J. 112 (2002), no. 3, 521-579 https://doi.org/10.1215/S0012-9074-02-11235-6
  2. A. Ash and W. Sinnott, 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 (2000), no. 1, 1-24 https://doi.org/10.1215/S0012-7094-00-10511-X
  3. S. Brueggeman, The nonexistence of certain Galois extensions unramified outside 5, J. Number Theory 75 (1999), no. 1, 47-52 https://doi.org/10.1006/jnth.1998.2318
  4. J. Jones, Tables of number fields with prescribed ramification, http://math.la.asu.edu/~jj/numberfields, 1998
  5. C. Khare, Serre's modularity conjecture: the level one case, Duke Math. J. 134 (2006), no. 3, 557-589 https://doi.org/10.1215/S0012-7094-06-13434-8
  6. H. Moon, Finiteness results on certain mod p Galois representations, J. Number Theory 84 (2000), no. 1, 156-165 https://doi.org/10.1006/jnth.2000.2534
  7. A. M. Odlyzko, Discriminant bounds, tables dated Nov. 29, 1976, unpublished, appeared in http://www.dtc.umn/~odlyzko/unpublished/discr.bound.table2
  8. J.-P. Serre, Sur les representations modulaires de degre 2 de Gal $(\bar{Q}/Q)$, Duke Math. J. 54 (1987), 179-230 https://doi.org/10.1215/S0012-7094-87-05413-5
  9. J. Tate, The non-existence of certain Galois extensions of Q unramified outside 2, Arithmetic geometry (Tempe, AZ, 1993), 153-156, Contemp. Math., 174, Amer. Math. Soc., Providence, RI, 1994