A note on Tannakian categories and mixed motives

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 étale motives over F with integral coefficients, up to the tensor triangulated structure, in terms of the characteristic and the orderings of F.

13 pages; v2: published version

References in corpus (5)

• The frame of smashing tensor-ideals
• The spectrum of prime ideals in tensor triangulated categories
• Three real Artin-Tate motives
• tt-geometry of filtered modules
• tt-geometry of Tate motives over algebraically closed fields

Cited by in corpus (1)

• Tensor structure on perverse Nori motives