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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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