Motivic Galois representations valued in Spin groups
Journal de Théorie des Nombres de Bordeaux, Tome 33 (2021) no. 1, pp. 197-221.

Soit m un entier tel que m7 et m0,1,7mod8. Nous construisons des systèmes strictement compatibles de repré- sentations l-adiques Γ Spin m ( ¯ l ) spinGL N ( ¯ l ) qui sont potentiellement automorphes et motiviques. Comme application, dans certains cas nous donnons une réponse positive au problème de Galois inverse pour les groupes spinoriels sur 𝔽 p . Pour m impair, nous comparons nos exemples avec le travail de A. Kret et S. W. Shin ([18]), qui étudie les représentations galoisiennes automorphes à valeurs dans GSpin m .

Let m be an integer such that m7 and m0,1,7mod8. We construct strictly compatible systems of representations of Γ Spin m ( ¯ l ) spinGL N ( ¯ 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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DOI : https://doi.org/10.5802/jtnb.1157
Classification : 11F80
Mots clés : Galois representations, spin groups, inverse Galois problem, automorphic representations
@article{JTNB_2021__33_1_197_0,
     author = {Shiang Tang},
     title = {Motivic {Galois} representations valued in {Spin} groups},
     journal = {Journal de Th\'eorie des Nombres de Bordeaux},
     pages = {197--221},
     publisher = {Soci\'et\'e Arithm\'etique de Bordeaux},
     volume = {33},
     number = {1},
     year = {2021},
     doi = {10.5802/jtnb.1157},
     language = {en},
     url = {https://jtnb.centre-mersenne.org/articles/10.5802/jtnb.1157/}
}
Shiang Tang. Motivic Galois representations valued in Spin groups. Journal de Théorie des Nombres de Bordeaux, Tome 33 (2021) no. 1, pp. 197-221. doi : 10.5802/jtnb.1157. https://jtnb.centre-mersenne.org/articles/10.5802/jtnb.1157/

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