Ash, Avner; McConnell, Mark Experimental indications of three-dimensional Galois representations from the cohomology of \(\text{SL}(3,\mathbb Z)\). (English) Zbl 0780.11029 Exp. Math. 1, No. 3, 209-223 (1992). The authors found Hecke eigenclasses in the mod \(p\) cohomology of certain congruence subgroups of \(\text{SL}(3,\mathbb Z)\) by computer computation. They then searched for three-dimensional Galois representations attached to the Hecke eigenclasses as predicted by a conjecture [cf. A. Ash, Duke Math. J. 65, 235–255 (1992; Zbl 0774.11024)]. After checking the conjecture at infinity and at primes up to 97, they found evidence that the conjecture might be true for \(n=3\). Reviewer: Y.Ye (Iowa City) Cited in 3 ReviewsCited in 19 Documents MSC: 11F75 Cohomology of arithmetic groups 11Y40 Algebraic number theory computations 11F80 Galois representations Keywords:Hecke eigenclasses; cohomology; congruence subgroups of \(\text{SL}(3,\mathbb Z)\); three-dimensional Galois representations Citations:Zbl 0774.11024 PDFBibTeX XMLCite \textit{A. Ash} and \textit{M. McConnell}, Exp. Math. 1, No. 3, 209--223 (1992; Zbl 0780.11029) Full Text: DOI EuDML EMIS References: [1] Ash A., Séminaire de Théorie des Nombres. Paris, 1989–90 (1992) [2] Ash A., Duke Math. J. 65 pp 235– (1992) · Zbl 0774.11024 [3] Ash A., J. Number Theory 19 pp 412– (1984) · Zbl 0552.10015 [4] Ash A., Math. Ann. 291 pp 753– (1991) · Zbl 0713.11036 [5] Ash A., J. Reine Angew. Math. 365 pp 192– (1986) [6] Bloom D., Trans. Amir. Math. Soc. 127 pp 150– (1967) [7] Buhler J., Icosahedral Galois Representations. (1978) · Zbl 0374.12002 [8] Clozel, L. ”Motifs et formes automorphes: applications du principe de fonctorialité”. Automorphic Forms, Shimura Varieties and L-functions. Proceedings of the Ann Arbor Conference. Edited by: Clozel, L. and Milne, J. S. vol. 1, pp.77–159. New York: Academic Press. [Clozel 1990] [9] Crespo T., J. Algebra 127 pp 452– (1989) · Zbl 0704.11043 [10] Deligne P., Séminaire Bourbaki 355 pp 139– (1971) [11] Delone B., The Theory of Irrationalities of the Third Degree (1964) · Zbl 0133.30202 [12] Gras M., J. Reine Angew. Math. 277 pp 89– (1975) [13] Mitchell H. H., Trans. Amer. Math. Soc. 12 pp 207– (1911) [14] Pohst M., Algorithmic Algebraic Number Theory. (1989) · Zbl 0685.12001 [15] Serre J.-P., Comment. Math. Helvetici 59 pp 651– (1984) · Zbl 0565.12014 [16] Serre J.-P., Duke Math. J. 54 pp 179– (1987) · Zbl 0641.10026 [17] Shimura G., Introduction to the Arithmetic Theory of Automorphic Functions (1971) · Zbl 0221.10029 This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.