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Divisible Motives and Tate's Conjecture
2011
International mathematics research notices
This article gives an analog of Taylor's trick in the context of motives for absolute Hodge cycles. The aforementioned trick, first sketched by Taylor in a letter to Clozel, gives two conditions ensuring that an mn-dimensional -adic Galois representation is divisible by m. We give a detailed proof of this result, and extend it to motives by using Tannakian duality.
doi:10.1093/imrn/rnr168
fatcat:mllwnq7lunaavmncjyibwwk7te