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, Tome 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 Γℚ→Spinm(ℚ¯l)→spinGLN(ℚ¯l) that are potentially automorphic and motivic. As an application, we prove instances of the inverse Galois problem for the 𝔽p–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 GSpinm.

Soit m un entier tel que m≥7 et m≡0,1,7mod8. Nous construisons des systèmes strictement compatibles de repré- sentations l-adiques Γℚ→Spinm(ℚ¯l)→spinGLN(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 𝔽p. 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 GSpinm.

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Accepté le :
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DOI : 10.5802/jtnb.1157
Classification : 11F80
Mots-clés : Galois representations, spin groups, inverse Galois problem, automorphic representations

Shiang Tang 1

1 1409 West Green Street Urbana, IL 61801, United States
Licence : CC-BY-ND 4.0
Droits d'auteur : Les auteurs conservent leurs droits 
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     title = {Motivic {Galois} representations valued in {Spin} groups},
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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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