Rigid Local Systems and Potential Automorphy: the G 2 -case
نویسنده
چکیده
For s ∈ P(Q) \ {0, 1}, we study the compatible system of Galois representations (ρ l (3) : Gal(Q̄/Q) → G2(Ql))l introduced in [4], where G2(Ql) ≤ GL7(Ql) is the simple group of type G2. We prove that, under some mild condition on s, the image of the Tate twisted Galois representation ρ l (3) coincides with G2(Zl) for all l up to a set of primes having density zero, and we show that ρ l is potentially automorphic for all l. From this, meromorphic continuation and functional equation for the L-function of ρ l is deduced.
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