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Algebraic \(K\)-theory, motives, and algebraic cycles. (English) Zbl 0759.14001
Proc. Int. Congr. Math., Kyoto/Japan 1990, Vol. I, 43-54 (1991).
[For the entire collection see Zbl 0741.00019.]
Based on work of Deligne on mixed Hodge structure Beilinson introduced mixed motives, the setting of this paper. A moving-lemma and consequences relating higher Chow groups to \(K_ 0\) in the \(K\)-theory of coherent sheaves were conjectured. Some initial possibilities for mixed Tate motives are considered. Arithmetic consequences are motivated.

MSC:
14A20 Generalizations (algebraic spaces, stacks)
14C25 Algebraic cycles
14C30 Transcendental methods, Hodge theory (algebro-geometric aspects)
14C35 Applications of methods of algebraic \(K\)-theory in algebraic geometry
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