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).
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CALTECH, Dept Math, Mail Code 253-37,1200 E Calif Blvd, Pasadena, CA 91125 USACALTECH, Dept Math, Mail Code 253-37,1200 E Calif Blvd, Pasadena, CA 91125 USA
Marcolli, Matilde
Tabuda, Goncalo
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MIT, Dept Math, Cambridge, MA 02139 USA
Univ Nova Lisboa, Dept Matemat FCT, Lisbon, Portugal
Univ Nova Lisboa, FCT, Ctr Matemat & Aplicacoes, Lisbon, PortugalCALTECH, Dept Math, Mail Code 253-37,1200 E Calif Blvd, Pasadena, CA 91125 USA
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Univ Amsterdam, Korteweg de Vries Inst, Sci Pk 105, NL-1090 GE Amsterdam, NetherlandsUniv Amsterdam, Korteweg de Vries Inst, Sci Pk 105, NL-1090 GE Amsterdam, Netherlands
Kret, Arno
Shin, Sug Woo
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Univ Calif Berkeley, Dept Math, Berkeley, CA 94720 USA
Korea Inst Adv Study, 85 Hoegiro, Seoul 130722, South KoreaUniv Amsterdam, Korteweg de Vries Inst, Sci Pk 105, NL-1090 GE Amsterdam, Netherlands