Abstract
We give axioms for a triangulated ℚ-tensor category T, generated by “Tate objects” ℚ(a), which ensure the existence of a canonical weight filtration on T, and additional axioms which give rise to an abelian subcategory A generated by the ℚ(a). We show in addition that A is a Tannakian category, with fiber functor to graded ℚ-vectorspaces given by taking the associated graded with respect to the weight filtration. We then apply this to our construction of a triangulated motivic category over a field k, to show that, assuming the vanishing conjectures of Soulé and Beilinson are true for k, there is a Tannakian category TM k which has many of the properties of the conjectural category of mixed Tate motives. In particular, the category TM k exists for k a number field.
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© 1993 Springer Science+Business Media Dordrecht
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Levine, M. (1993). Tate Motives and the Vanishing Conjectures for Algebraic K-Theory. In: Goerss, P.G., Jardine, J.F. (eds) Algebraic K-Theory and Algebraic Topology. NATO ASI Series, vol 407. Springer, Dordrecht. https://doi.org/10.1007/978-94-017-0695-7_7
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DOI: https://doi.org/10.1007/978-94-017-0695-7_7
Publisher Name: Springer, Dordrecht
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