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