Tate Motives and the Vanishing Conjectures for Algebraic K-Theory

Part of the NATO ASI Series book series (ASIC, volume 407)


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.


Exact Sequence Short Exact Sequence Full Subcategory Tensor Category Weight Filtration 
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Copyright information

© Springer Science+Business Media Dordrecht 1993

Authors and Affiliations

  1. 1.Department of MathematicsNortheastern UniversityBostonUSA

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