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arXiv · 2505.06979

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

Maxime Ramzi·Maria Yakerson
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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.

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Maxime Ramzi, Maria Yakerson. 2025-05-11. $p$-perfection and group completion of $\mathbb{E}_\infty$-monoids. https://arxiv.org/abs/2505.06979

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