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Tate Motives and the Vanishing Conjectures for Algebraic K-Theory

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

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.

Keywords

Exact Sequence Short Exact Sequence Full Subcategory Tensor Category Weight Filtration 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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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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