Motives with Galois Group of Type G2: an Exceptional Theta-correspondence
نویسندگان
چکیده
Serre has asked if there are motives M with motivic Galois group of type G2 [Se3; pg 386]. This paper is the first step in a project to construct such a motive M , of rank 7 and weight 0, over the base field Q. Let G be the anisotropic form of G2 over Q, and let π = ⊗̂vπv be an automorphic representation of the adelic group G(A). At almost all primes p, the local representation πp is unramified and has Satake parameter sp, a semi-simple conjugacy class in the dual group Ĝ(C) = G2(C). Let V̂ be the irreducible 7-dimensional representation of Ĝ(C). The unramified representation πp is determined by the characteristic polynomial of sp on V̂:
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