Let m be an integer such that m >= 7 and m equivalent to 0, 1, 7 mod 8. We construct strictly compatible systems of representations of Gamma(Q) -> Spin(m) ((Q) over bar (l)) spin ->(spin) GL(N) ((Q) over bar (l)) that are potentially automorphic and motivic. As an application, we prove instances of the inverse Galois problem for the F-p-points of the spin groups. For odd m, we compare our examples with the work of A. Kret and S. W. Shin ([18]), which studies automorphic Galois representations valued in GSpin(m).
机构:
Univ Barcelona, Dept Algebra & Geometria, Gran Via Corts Catalanes 585, Barcelona 08007, SpainUniv Barcelona, Dept Algebra & Geometria, Gran Via Corts Catalanes 585, Barcelona 08007, Spain
Dieulefait, Luis
Zenteno, Adrian
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UNAM, Inst Matemat, Av Univ S-N, Cuernavaca 62210, Morelos, MexicoUniv Barcelona, Dept Algebra & Geometria, Gran Via Corts Catalanes 585, Barcelona 08007, Spain