Motivic Galois representations valued in Spin groups
Shiang Tang1
1 1409 West Green Street Urbana, IL 61801, United States
Journal de théorie des nombres de Bordeaux, Volume 33 (2021) no. 1, pp. 197-221.

Let m be an integer such that m≥7 and m≡0,1,7mod8. We construct strictly compatible systems of representations of Γ ℚ →Spin m (ℚ ¯ l )→ spinGL N (ℚ ¯ 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 .

Soit m un entier tel que m≥7 et m≡0,1,7mod8. Nous construisons des systèmes strictement compatibles de repré- sentations l-adiques Γ ℚ →Spin m (ℚ ¯ l )→ spinGL N (ℚ ¯ 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 .

Received:
Accepted:
Published online:
DOI: 10.5802/jtnb.1157
Classification: 11F80
Keywords: Galois representations, spin groups, inverse Galois problem, automorphic representations

Shiang Tang 1

1 1409 West Green Street Urbana, IL 61801, United States
License: CC-BY-ND 4.0
Copyrights: The authors retain unrestricted copyrights and publishing rights 
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Shiang Tang. Motivic Galois representations valued in Spin groups. Journal de théorie des nombres de Bordeaux, Volume 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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