Direct sums of mod p characters of Gal(Q̄/Q) and the homology of GLn(Z)
نویسنده
چکیده
We prove the following theorem: Let F be an algebraic closure of a finite field of characteristic p. If ρ is a continuous homomorphism from the absolute Galois group of Q to GLn(F) which is isomorphic to a direct sum of one-dimensional representations, and if p > n+1 and the conductors of the one-dimensional representations are pairwise relatively prime, and if a certain parity condition holds, then ρ is attached to a Hecke eigenclass in the homology of an arithmetic subgroup Γ of SL(n,Z) with coefficients in a certain module V . Moreover, Γ and V are as predicted by Conjecture 2.2 of [5].
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