Galois Representations, Hecke Operators, and the mod-p Cohomology of GL(3, Z) with Twisted Coefficients
- 1 January 1998
- journal article
- research article
- Published by Taylor & Francis in Experimental Mathematics
- Vol. 7 (4) , 361-390
- https://doi.org/10.1080/10586458.1998.10504381
Abstract
We compute the degree 3 homology of Gl(3, Z) with coefficients in the module of homogeneous polynomials in three variables of degree g over Fp, for g ≤ 200 and p ≤ 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, p). The conjecture is proved for the boundary part and explored experimentally for the quasicuspidal part.Keywords
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