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Duality via cycle complexes. (English) Zbl 1215.19001
In this paper the author proves a very hard theorem on the adjointness for a constructible sheaf and for the complex of étale sheaves constructed in a manner of Bloch’s defining higher Chow groups. By this theorem, the corresponding dualities of perfect pairings are also obtained, respectively, over a finite field, a local field, and a number ring.
The applications of these results can be taken, respectively, as generalizations of several known related theorems.

MSC:
19E15 Algebraic cycles and motivic cohomology (\(K\)-theoretic aspects)
14F42 Motivic cohomology; motivic homotopy theory
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References:
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