Gerbes and abelian motives

J. S. Milne

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arXiv · math/0301304

Gerbes and abelian motives

J. S. Milne

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Abstract

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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J. S. Milne. 2003-01-26. Gerbes and abelian motives. https://arxiv.org/abs/math/0301304

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