## $$\mathrm{SL}_3(\mathbb F_2)$$-extensions of $$\mathbb Q$$ and arithmetic cohomology modulo 2.(English)Zbl 1094.11019

In [A. Ash, D. Doud and D. Pollack, Duke Math. J. 112, No. 3, 521–579 (2002; Zbl 1023.11025)] there is presented the conjecture that every mod-$$p$$ Galois representation in $$\mathrm{GL}_n$$ should be attached to the mod-$$p$$ cohomology of the arithmetic group $$\Gamma_0 (N)$$ in the sense that Frobenius eigenvalues correspond to Hecke eigenvalues. For $$n=2$$ this conjecture boils down to Serre’s classical conjecture. The conjecture is tested numerically in many cases when $$p$$ is an odd prime.
In the paper under review the authors test the conjecture for $$p=2$$, and they offer a refinement of the conjecture resolving ambiguities in the predicted weight.

### MSC:

 11F75 Cohomology of arithmetic groups 11F80 Galois representations 11F70 Representation-theoretic methods; automorphic representations over local and global fields

### Keywords:

cohomology of arithmetic groups

Zbl 1023.11025
Full Text:

### References:

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