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15 April 2020 Maximality of Galois actions for abelian and hyper-Kähler varieties
Chun Yin Hui, Michael Larsen
Duke Math. J. 169(6): 1163-1207 (15 April 2020). DOI: 10.1215/00127094-2019-0054

Abstract

Let {ρ} be the system of -adic representations arising from the ith -adic cohomology of a proper smooth variety X defined over a number field K. Let Γ and G be, respectively, the image and the algebraic monodromy group of ρ. We prove that the reductive quotient of G is unramified over every degree 12 totally ramified extension of Q for all sufficiently large . We give a necessary and sufficient condition (*) on {ρ} such that, for all sufficiently large , the subgroup Γ is in some sense maximal compact in G(Q). This is used to deduce Galois maximality results for -adic representations arising from abelian varieties (for all i) and hyper-Kähler varieties (i=2) defined over finitely generated fields over Q.

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Chun Yin Hui. Michael Larsen. "Maximality of Galois actions for abelian and hyper-Kähler varieties." Duke Math. J. 169 (6) 1163 - 1207, 15 April 2020. https://doi.org/10.1215/00127094-2019-0054

Information

Received: 22 September 2017; Revised: 13 May 2019; Published: 15 April 2020
First available in Project Euclid: 1 April 2020

zbMATH: 07198474
MathSciNet: MR4085080
Digital Object Identifier: 10.1215/00127094-2019-0054

Subjects:
Primary: 11F80
Secondary: 11G10, 20G30

Rights: Copyright © 2020 Duke University Press

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Vol.169 • No. 6 • 15 April 2020
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