Rigid G2-representations and motives of type G2 - Dettweiler, Michael; Schmidt, Johannes (Israel journal of mathematics, 2016)
We consider a family of motives associated to the rigid local system whose monodromy is dense in the simple algebraic group of type G 2 and which has a local monodromy of order 7 at ∞ . We prove an explicit Hilbert irreduciblity theorem for the associated étale realizations and deduce that the specialized motives at the points of irreducibility have motivic Galois group G 2.
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