Gerbes and abelian motives
Algebraic Geometry
2007-05-23 v1 Number Theory
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.
Keywords
Cite
@article{arxiv.math/0301304,
title = {Gerbes and abelian motives},
author = {J. S. Milne},
journal= {arXiv preprint arXiv:math/0301304},
year = {2007}
}