Cohomology of presheaves with oriented weak transfers

2014/05/01 by Joseph Ross, Ross, Joseph
Mathematics · #FOS: Mathematics #K-Theory and Homology (math.KT) #math.KT

paper · pdf · doi:10.48550/arxiv.1405.0176

Comments welcome!

arxiv created 2014/05/01 · arxiv updated 2014/05/02

Abstract

Over a field of characteristic zero, we establish the homotopy invariance of the Nisnevich cohomology of homotopy invariant presheaves with oriented weak transfers, and the agreement of Zariski and Nisnevich cohomology for such presheaves. This generalizes a foundational result in Voevodsky's theory of motives. The main idea is to find explicit smooth representatives of the correspondences which provide the input for Voevodsky's cohomological architecture.

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