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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.

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