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The construction of weight-two arithmetic cohomology. (English) Zbl 0615.14004
One constructs for any regular noetherian scheme X a two-term complex $$\Gamma$$ (2,X) of sheaves in the étale topology which is acyclic outside of [1,2] and whose hypercohomology sheaves $${\mathcal H}^ 1$$ and $${\mathcal H}^ 2$$ are related to the algebraic K-theory as classical cohomology is related to topological K-theory. In specific situations these $${\mathcal H}^ i$$ have arithmetic properties.
The construction solves at weight-two level a conjecture done by Beilinson for Zariski topology and extended by the author to the étale topology and moreover completed with arithmetic features.
Reviewer: M.Stoia

MSC:
 14C35 Applications of methods of algebraic $$K$$-theory in algebraic geometry 18F25 Algebraic $$K$$-theory and $$L$$-theory (category-theoretic aspects)
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References:
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