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ℂ-Motivic Eilenberg-Mac Lane Spectra as MGL-Motivic Thom Spectra and Normed 𝔾m-Hochschild Homology
Abstract
We exhibit the p-complete ℂ-motivic Eilenberg-Mac Lane spectra M𝔽p and (Mℤ)p∧ as 𝔼_3-MGLp∧-motivic Thom spectra over the motivic 𝔾m-loop spaces Ω𝔾mBGL and Ω𝔾mBSL, respectively. Furthermore, for p=2, we compute the MGL2∧-relative 𝔾m-Hochschild Homology 𝔾m ⊙MGL2∧ −, recently introduced by Bachmann-Burklund-Dundas-Østvær, of M𝔽2 and (Mℤ)2∧ to be M𝔽2[BGL] and (Mℤ)2∧[BSL] as 𝔼2-M𝔽2-algebras and 𝔼2-(Mℤ)2∧-algebras, respectively.
Related
BibTeX
@misc{cranford2026ℂmotivic,
title = {{$\mathbbC$-Motivic Eilenberg-Mac Lane Spectra as $\mathrmMGL$-Motivic Thom Spectra and Normed $\mathbbG_m$-Hochschild Homology}},
author = {Preston Cranford},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.26771},
eprint = {2610.26771},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.26771},
}
RIS
TY - UNPB
TI - ℂ-Motivic Eilenberg-Mac Lane Spectra as MGL-Motivic Thom Spectra and Normed 𝔾_m-Hochschild Homology
AU - Preston Cranford
PY - 2026
DA - 2026/10/19
PB - arXiv
DO - 10.48550/arxiv.2610.26771
UR - https://arxiv.org/abs/2610.26771
AB - We exhibit the p-complete ℂ-motivic Eilenberg-Mac Lane spectra M𝔽_p and (Mℤ)_p^∧ as 𝔼_3-MGL_p^∧-motivic Thom spectra over the motivic 𝔾_m-loop spaces Ω_𝔾_mBGL and Ω_𝔾_mBSL, respectively. Furthermore, for p=2, we compute the MGL_2^∧-relative 𝔾_m-Hochschild Homology 𝔾_m ⊙^MGL_2^∧ −, recently introduced by Bachmann-Burklund-Dundas-Østvær, of M𝔽_2 and (Mℤ)_2^∧ to be M𝔽_2[BGL] and (Mℤ)_2^∧[BSL] as 𝔼_2-M𝔽_2-algebras and 𝔼_2-(Mℤ)_2^∧-algebras, respectively.
ER -