Cohomology of presheaves with oriented weak transfers

Ross, Joseph

doi:10.1090/jag/684

Author: Joseph Ross
Journal: J. Algebraic Geom. 26 (2017), 557-602
DOI: https://doi.org/10.1090/jag/684
Published electronically: November 23, 2016
MathSciNet review: 3647793
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Abstract | References | Additional Information

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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Additional Information

Joseph Ross
Affiliation: Department of Mathematics, University of Southern California, 3620 South Vermont Avenue, Los Angeles, California 90089-0894
MR Author ID: 891309
Email: joseph.ross@gmail.com

Received by editor(s): February 26, 2015
Received by editor(s) in revised form: November 8, 2015
Published electronically: November 23, 2016
Article copyright: © Copyright 2016 University Press, Inc.