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The multiplicative structures on motivic homotopy groups

Daniel Dugger, Bjørn Ian Dundas, Daniel C Isaksen and Paul Arne Østvær

Algebraic & Geometric Topology 24 (2024) 1781–1786
Abstract

We reconcile the multiplications on the homotopy rings of motivic ring spectra used by Voevodsky and Dugger. While the connection is elementary and similar phenomena have been observed in situations like supersymmetry, neither we nor other researchers we consulted were aware of the conflicting definitions and the potential consequences. Hence this short note.

Keywords
graded commutativity, motivic ring spectra, Betti realization
Mathematical Subject Classification
Primary: 14F42
Secondary: 13A02
References
Publication
Received: 7 December 2022
Revised: 14 December 2022
Accepted: 3 January 2023
Published: 28 June 2024
Authors
Daniel Dugger
Department of Mathematics
University of Oregon
Eugene, OR
United States
Bjørn Ian Dundas
Department of Mathematics
University of Bergen
Bergen
Norway
Daniel C Isaksen
Department of Mathematics
Wayne State University
Detroit, MI
United States
Paul Arne Østvær
Department of Mathematics F Enriques
University of Milan
Milan
Italy
Department of Mathematics
University of Oslo
Oslo
Norway

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