Gerbes and abelian motives

Details Gerbes and abelian motives Gerbes and abelian motives

2003-01-26

arxiv.org/abs/math/0301304v1

Mathematics

Algebraic Geometry

Scientific paper

Assuming the Hodge conjecture for abelian varieties of CM-type, one obtains a good category of abelian motives over the algebraic closure of a finite field and a reduction functor to it from the category of CM-motives. Consequentely, one obtains a morphism of gerbes of fibre functors with certain properties. We prove unconditionally that there exists a morphism of gerbes with these properties, and we classify them.

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