Motives over Fp
Abstract
In April, 2006, Kontsevich asked me whether the category of motives over Fp (p prime) has a fibre functor over a number field of finite degree since he had a conjecture that more-or-less implied this. This article is my response. Unfortunately, since the results are generally negative or inconclusive, they are of little interest except perhaps for the question they raise on the existence of a cyclic extension of Q having certain properties.
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