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Constant spectral Mackey functors and the equivariant Steenrod algebra
Abstract
For a finite group G, we define a constant spectral G-Mackey functor as a genuine G-spectrum in which the restrictions between categorical fixed points are equivalences. We further identify the full subcategory of constant spectral G-Mackey functors with the category of modules over a certain 𝔼1-ring spectrum RG. When G=Cpn is a cyclic p-group, we provide an explicit construction of the 𝔼1-ring spectrum RCpn. The proof uses a reconstruction theorem for genuine Cpn-spectra, which might be of independent interest. As an application, we compute the ℤ-graded Cpn-equivariant mod p Steenrod algebra.
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BibTeX
@misc{pan2026constant,
title = {{Constant spectral Mackey functors and the equivariant Steenrod algebra}},
author = {Kailin Pan},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.05654},
eprint = {2610.05654},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.05654},
}
RIS
TY - UNPB
TI - Constant spectral Mackey functors and the equivariant Steenrod algebra
AU - Kailin Pan
PY - 2026
DA - 2026/10/05
PB - arXiv
DO - 10.48550/arxiv.2610.05654
UR - https://arxiv.org/abs/2610.05654
AB - For a finite group G, we define a constant spectral G-Mackey functor as a genuine G-spectrum in which the restrictions between categorical fixed points are equivalences. We further identify the full subcategory of constant spectral G-Mackey functors with the category of modules over a certain 𝔼_1-ring spectrum R_G. When G=C_p^n is a cyclic p-group, we provide an explicit construction of the 𝔼_1-ring spectrum R_C_p^n. The proof uses a reconstruction theorem for genuine C_p^n-spectra, which might be of independent interest. As an application, we compute the ℤ-graded C_p^n-equivariant mod p Steenrod algebra.
ER -