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Absolute cohomological purity. (English) Zbl 0584.14007

The paper provides a good framework for present day investigation into Grothendieck’s purity conjecture. Grothendieck’s purity conjecture is proven for the \({\mathbb{Q}}^{\wedge}_{\ell}\)-étale cohomology and for étale cohomology with \({\mathbb{Z}}/\ell^{\nu}\) coefficients if \(\ell\) is large. The results are corollaries of Quillen’s localization theorem for algebraic K-theory and the author’s own comparison of topological and algebraic K-theory.
Reviewer: P.Cherenack

MSC:

14F20 Étale and other Grothendieck topologies and (co)homologies
14C35 Applications of methods of algebraic \(K\)-theory in algebraic geometry
14G99 Arithmetic problems in algebraic geometry; Diophantine geometry
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