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arXiv · 1912.12483

A note on Tannakian categories and mixed motives

Martin Gallauer
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Abstract

We explain why every non-trivial exact tensor functor on the triangulated category of mixed motives over a field F has zero kernel, if one assumes "all" motivic conjectures. In other words, every non-zero motive generates the whole category up to the tensor triangulated structure. Under the same assumptions, we also give a complete classification of triangulated \'etale motives over F with integral coefficients, up to the tensor triangulated structure, in terms of the characteristic and the orderings of F.

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Martin Gallauer. 2019-12-28. A note on Tannakian categories and mixed motives. https://doi.org/10.1112/blms.12405

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