PreprintCC BY 4.0arXiv
Motivic Cp-power operations in MGL
Abstract
In this paper, we give a new proof of the Hopkins-Morel-Hoyois theorem for fields k of characteristic unequal to p containing all primitive p-power roots of unity for a fixed prime p. This new proof follows Quillen's proof for the structure of the homotopy groups of MU which utilizes topological power operations. To this end we define a motivic analog of the Steenrod power operations, using the theory of normed motivic spectra as developed by Bachmann--Hoyois and their application for the definition of motivic colimits as developed by Bachmann-Elmanto-Heller.
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BibTeX
@misc{tausendpfund2026motivic,
title = {{Motivic $C_p$-power operations in $\mathrmMGL$}},
author = {Timon Tausendpfund},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.35903},
eprint = {2610.35903},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.35903},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Motivic C_p-power operations in MGL
AU - Timon Tausendpfund
PY - 2026
DA - 2026/10/01
PB - arXiv
DO - 10.48550/arxiv.2610.35903
UR - https://arxiv.org/abs/2610.35903
AB - In this paper, we give a new proof of the Hopkins-Morel-Hoyois theorem for fields k of characteristic unequal to p containing all primitive p-power roots of unity for a fixed prime p. This new proof follows Quillen's proof for the structure of the homotopy groups of MU which utilizes topological power operations. To this end we define a motivic analog of the Steenrod power operations, using the theory of normed motivic spectra as developed by Bachmann--Hoyois and their application for the definition of motivic colimits as developed by Bachmann-Elmanto-Heller.
ER -