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THE TOM DIECK SPLITTING THEOREM IN EQUIVARIANT MOTIVIC HOMOTOPY THEORY

Part of: Homotopy theory (Co)homology theory

Published online by Cambridge University Press:  10 November 2021

David Gepner Open the ORCID record for David Gepner [Opens in a new window]  and
Jeremiah Heller
David Gepner*
Affiliation:
Johns Hopkins University, Department of Mathematics, 404 Krieger Hall, 3400 N. Charles Street, Baltimore, MD 21218, USA
Jeremiah Heller
Affiliation:
University of Illinois at Urbana-Champaign, Department of Mathematics, 1409 W. Green Street, Urbana, IL 61801, USA (jbheller@illinois.edu)
*
dgepner1@jhu.edu
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Abstract

We establish, in the setting of equivariant motivic homotopy theory for a finite group, a version of tom Dieck’s splitting theorem for the fixed points of a suspension spectrum. Along the way we establish structural results and constructions for equivariant motivic homotopy theory of independent interest. This includes geometric fixed-point functors and the motivic Adams isomorphism.

Keywords

motivic homotopy theoryequivariant homotopy theoryAdams isomorphismtom Dieck splitting

MSC classification

Primary: 14F42: Motivic cohomology; motivic homotopy theory 55P91: Equivariant homotopy theory
Secondary: 55P42: Stable homotopy theory, spectra 55P92: Relations between equivariant and nonequivariant homotopy theory
Type
Research Article
Information
Journal of the Institute of Mathematics of Jussieu , Volume 22 , Issue 3 , May 2023 , pp. 1181 - 1250
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Copyright
© The Author(s), 2021. Published by Cambridge University Press

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