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1998 Galois representations, Hecke operators, and the mod-$p$ cohomology of ${\rm GL}(3,\mathbb Z)$ with twisted coefficients
Gerald Allison, Avner Ash, Eric Conrad
Experiment. Math. 7(4): 361-390 (1998).

Abstract

We compute the degree 3 homology of GL(3,\,\funnyZ) with coefficients in the module of homogeneous polynomials in three variables of degree $g$ over $\mathbb F_p$, for $g\leq 200$ and $p\leq 541$. The homology has a "boundary part'' and a "quasicuspidal'' part which we determine.

By conjecture a Hecke eigenclass in the homology has an attached Galois representation into $GL(3,\,\bar{\mathbb F}_p$). The conjecture is proved for the boundary part and explored experimentally for the quasicuspidal part.

Citation

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Gerald Allison. Avner Ash. Eric Conrad. "Galois representations, Hecke operators, and the mod-$p$ cohomology of ${\rm GL}(3,\mathbb Z)$ with twisted coefficients." Experiment. Math. 7 (4) 361 - 390, 1998.

Information

Published: 1998
First available in Project Euclid: 14 March 2003

zbMATH: 0923.11083
MathSciNet: MR1678079

Subjects:
Primary: 11F80
Secondary: 11F60, 11F75, 11R39

Rights: Copyright © 1998 A K Peters, Ltd.

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Vol.7 • No. 4 • 1998
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