Galois representations, Hecke operators, and the mod-{$p$} cohomology of {${\rm GL}(3,\bold Z)$} with twisted coefficients
Allison, Gerald ; Ash, Avner ; Conrad, Eric
Experiment. Math., Tome 7 (1998) no. 4, p. 361-390 / Harvested from Project Euclid
Text on Project Euclid
PDF
Alt PDF
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 \funnyF$_p$, 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,\,{\mathversion{normal}$\bar{\funnyF}$}$_p$). The conjecture is proved for the boundary part and explored experimentally for the quasicuspidal part.
Publié le : 1998-05-14
Classification:  Galois representations,  Hecke operators,  mod-$p$ cohomology,  modular symbols,  11F80,  11F60,  11F75,  11R39 
@article{1047674153,
     author = {Allison, Gerald and Ash, Avner and Conrad, Eric},
     title = {Galois representations, Hecke operators, and the mod-{$p$} cohomology of {${\rm GL}(3,\bold Z)$} with twisted coefficients},
     journal = {Experiment. Math.},
     volume = {7},
     number = {4},
     year = {1998},
     pages = { 361-390},
     language = {en},
     url = {http://dml.mathdoc.fr/item/1047674153}
}

Allison, Gerald; Ash, Avner; Conrad, Eric. Galois representations, Hecke operators, and the mod-{$p$} cohomology of {${\rm GL}(3,\bold Z)$} with twisted coefficients. Experiment. Math., Tome 7 (1998) no. 4, pp.  361-390. http://gdmltest.u-ga.fr/item/1047674153/