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Journal of Algebraic Geometry

Journal of Algebraic Geometry

Online ISSN 1534-7486; Print ISSN 1056-3911



Equivariant connective $K$-theory

Authors: Nikita A. Karpenko and Alexander S. Merkurjev
Journal: J. Algebraic Geom. 31 (2022), 181-204
Published electronically: October 28, 2021
MathSciNet review: 4372412
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Abstract | References | Additional Information

Abstract: For separated schemes of finite type over a field with an action of an affine group scheme of finite type, we construct the bi-graded equivariant connective $K$-theory mapping to the equivariant $K$-homology of Guillot and the equivariant algebraic $K$-theory of Thomason. It has all the standard basic properties as the homotopy invariance and localization. We also get the equivariant version of the Brown-Gersten-Quillen spectral sequence and study its convergence.

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Additional Information

Nikita A. Karpenko
Affiliation: Department of Mathematical & Statistical Sciences, University of Alberta, Edmonton, Alberta, Canada
MR Author ID: 290050

Alexander S. Merkurjev
Affiliation: Department of Mathematics, University of California, Los Angeles, California
MR Author ID: 191878
ORCID: 0000-0002-4447-1838

Received by editor(s): October 31, 2019
Received by editor(s) in revised form: June 9, 2020, and August 1, 2020
Published electronically: October 28, 2021
Additional Notes: A part of the work by the first author was done during his visit of the Institut des Hautes Etudes Scientifiques in September-October 2019. The second author was supported by the NSF grant DMS #1801530.
Article copyright: © Copyright 2021 University Press, Inc.