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Experimental indications of three-dimensional Galois representations from the cohomology of \(\text{SL}(3,\mathbb Z)\). (English) Zbl 0780.11029

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)

MSC:

11F75 Cohomology of arithmetic groups
11Y40 Algebraic number theory computations
11F80 Galois representations

Citations:

Zbl 0774.11024
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References:

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