Divisible Motives and Tate's Conjecture

Claus M. Sorensen
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