The construction of weight-two arithmetic cohomology
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.
scientific article; zbMATH DE number 3995852