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

Title & Authors
ON FOUR-DIMENSIONAL MOD 2 GALOIS REPRESENTATIONS AND A CONJECTURE OF ASH ET AL
Moon, Hyun-Suk;

Abstract
The non-existence is proved of four-dimensional mod 2 semisimple representations of Gal ($\ Keywords mod p Galois representation;Ashs conjecture;Odlyzkos bound; Language English Cited by References 1. A. Ash, D. Doud, and D. Pollack, Galois representations with conjectural connections to arithmetic cohomology, Duke Math. J. 112 (2002), no. 3, 521-579 2. A. Ash and W. Sinnott, An analogue of Serre's conjecture for Galois representations and Hecke eigenclasses in the mod-p cohomology of GL(n; Z), Duke Math. J. 105 (2000), no. 1, 1-24 3. S. Brueggeman, The nonexistence of certain Galois extensions unramified outside 5, J. Number Theory 75 (1999), no. 1, 47-52 4. J. Jones, Tables of number fields with prescribed ramification, http://math.la.asu.edu/~jj/numberfields, 1998 5. C. Khare, Serre's modularity conjecture: the level one case, Duke Math. J. 134 (2006), no. 3, 557-589 6. H. Moon, Finiteness results on certain mod p Galois representations, J. Number Theory 84 (2000), no. 1, 156-165 7. A. M. Odlyzko, Discriminant bounds, tables dated Nov. 29, 1976, unpublished, appeared in http://www.dtc.umn/~odlyzko/unpublished/discr.bound.table2 8. J.-P. Serre, Sur les representations modulaires de degre 2 de Gal$(\bar{Q}/Q)\$, Duke Math. J. 54 (1987), 179-230

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