$p$-perfection and group completion of $\mathbb{E}_{\infty}$-monoids

We study \mathbb{E}_{\infty} -monoids on which a prime p acts invertibly, which we call p -perfect, in the non-group-complete situation. In particular, we prove that in many examples, they almost embed in their group-completion.We further study the p -perfection functor, and describe it in terms of Quillen’s + -construction, similarly to group-completion. This gives an alternative description of the p -inverted higher algebraic K -theory of a ring.

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Publication Details

Journal
Documenta Mathematica
Published
2026-06-26
DOI
https://doi.org/10.4171/dm/1086
Primary Topic
Homotopy and Cohomology in Algebraic Topology
Type
preprint
Field-Weighted Citation Impact
0.00

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preprint

$p$-perfection and group completion of $\mathbb{E}_{\infty}$-monoids

Maria Yakerson, Maxime Ramzi
Documenta Mathematica
Homotopy and Cohomology in Algebraic Topology
preprint

$p$-perfection and group completion of $\mathbb{E}_{\infty}$-monoids

Maria Yakerson, Maxime Ramzi
preprint en

Abstract

We study \mathbb{E}_{\infty} -monoids on which a prime p acts invertibly, which we call p -perfect, in the non-group-complete situation. In particular, we prove that in many examples, they almost embed in their group-completion.We further study the p -perfection functor, and describe it in terms of Quillen’s + -construction, similarly to group-completion. This gives an alternative description of the p -inverted higher algebraic K -theory of a ring.

Documenta Mathematica
Centre National de la Recherche Scientifique (FR), Université Paris Cité (FR), University of Münster (DE), Institut de Mathématiques de Jussieu-Paris Rive Gauche (FR), Sorbonne Université (FR)
National Research Foundation, Danmarks Grundforskningsfond
Openalex Percentile: Top 93%
Homotopy and Cohomology in Algebraic Topology
DOIOpen Access PDFOpenAlex
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