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• W2972808510 abstract "Let {ρℓ}ℓ be the system of ℓ-adic representations arising from the ith ℓ-adic cohomology of a proper smooth variety X defined over a number field K. Let Γℓ and Gℓ be, respectively, the image and the algebraic monodromy group of ρℓ. We prove that the reductive quotient of Gℓ∘ is unramified over every degree 12 totally ramified extension of Qℓ for all sufficiently large ℓ. We give a necessary and sufficient condition (*) on {ρℓ}ℓ such that, for all sufficiently large ℓ, the subgroup Γℓ is in some sense maximal compact in Gℓ(Qℓ). This is used to deduce Galois maximality results for ℓ-adic representations arising from abelian varieties (for all i) and hyper-Kähler varieties (i=2) defined over finitely generated fields over Q." @default.
• W2972808510 created "2019-09-19" @default.
• W2972808510 creator A5006726529 @default.
• W2972808510 creator A5071113396 @default.
• W2972808510 date "2020-04-15" @default.
• W2972808510 modified "2023-10-18" @default.
• W2972808510 title "Maximality of Galois actions for abelian and hyper-Kähler varieties" @default.
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• W2972808510 doi "https://doi.org/10.1215/00127094-2019-0054" @default.
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