G-local systems on smooth projective curves are potentially automorphic

2016/09/12 by Böckle, Gebhard, Harris, Michael, Khare, Chandrashekhar +1 · 1 citation
#FOS: Mathematics #Number Theory (math.NT)

paper · doi:10.48550/arxiv.1609.03491

Abstract

Let X be a smooth, projective, geometrically connected curve over a finite field \mathbbF_q, and let G be a split semisimple algebraic group over \mathbbF_q. Its dual group G is a split reductive group over ℤ. Conjecturally, any l-adic G-local system on X (equivalently, any conjugacy class of continuous homomorphisms π₁(X) → G(ℚ_l)) should be associated to an everywhere unramified automorphic representation of the group G. We show that for any homomorphism π₁(X) → G(ℚ_l) of Zariski dense image, there exists a finite Galois cover Y → X over which the associated local system becomes automorphic.

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