$p$-perfection and group completion of $\mathbb{E}_\infty$-monoids
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arXiv
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| Hauptverfasser: | , |
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| Format: | Preprint |
| Veröffentlicht: |
2025
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| _version_ | 1866912370138284032 |
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| author | Ramzi, Maxime Yakerson, Maria |
| author_facet | Ramzi, Maxime Yakerson, Maria |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2505_06979 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | $p$-perfection and group completion of $\mathbb{E}_\infty$-monoids Ramzi, Maxime Yakerson, Maria K-Theory and Homology Algebraic Topology 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. |
| title | $p$-perfection and group completion of $\mathbb{E}_\infty$-monoids |
| topic | K-Theory and Homology Algebraic Topology |
| url | https://arxiv.org/abs/2505.06979 |