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1992 Experimental indications of three-dimensional Galois representations from the cohomology of {${\rm SL}(3,{\bf Z})$}
Avner Ash, Mark McConnell
Experiment. Math. 1(3): 209-223 (1992).

Abstract

Conjecturally, any "algebraic'' automorphic representation on $\GL(n)$ should have an $n$-dimensional Galois representation attached. Many examples of algebraic automorphic representations come from the cohomology over $\bold C$ of congruence subgroups of $\GL(n,\bold Z)$. On the other hand, the first author has conjectured that for any Hecke eigenclass in the mod $p$ cohomology of a congruence subgroup of $\GL(n,\Z)$ there should be an attached $n$-dimensional Galois representation.

By computer, we found Hecke eigenclasses in the mod $p$ cohomology of certain congruence subgroups of $\SL(3,\bold Z)$. In a range of examples, we then found a Galois representation (uniquely determined up to isomorphism by our data) that seemed to be attached to the Hecke eigenclass.

Citation

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Avner Ash. Mark McConnell. "Experimental indications of three-dimensional Galois representations from the cohomology of {${\rm SL}(3,{\bf Z})$}." Experiment. Math. 1 (3) 209 - 223, 1992.

Information

Published: 1992
First available in Project Euclid: 25 March 2003

zbMATH: 0780.11029
MathSciNet: MR1203875

Subjects:
Primary: 11F75
Secondary: 11F80

Rights: Copyright © 1992 A K Peters, Ltd.

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Vol.1 • No. 3 • 1992
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