$\mathbb{E}_{\infty}$-coalgebras and $p$-adic homotopy theory
Fuente:
arXiv
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| Autori principali: | , |
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| Natura: | Preprint |
| Pubblicazione: |
2024
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| _version_ | 1866909119881936896 |
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| author | Bachmann, Tom Burklund, Robert |
| author_facet | Bachmann, Tom Burklund, Robert |
| contents | We show that for any separably closed field $k$ of characteristic $p>0$, the canonical functor from nilpotent $p$-adic spaces to $\mathbb{E}_{\infty}$-coalgebras over $k$ (given by singular chains with coefficients in $k$) is fully faithful. We also identify the essential image of simply connected spaces inside coalgebras. This dualizes and removes finiteness assumptions from a theorem of Mandell. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2402_15850 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | $\mathbb{E}_{\infty}$-coalgebras and $p$-adic homotopy theory Bachmann, Tom Burklund, Robert Algebraic Topology We show that for any separably closed field $k$ of characteristic $p>0$, the canonical functor from nilpotent $p$-adic spaces to $\mathbb{E}_{\infty}$-coalgebras over $k$ (given by singular chains with coefficients in $k$) is fully faithful. We also identify the essential image of simply connected spaces inside coalgebras. This dualizes and removes finiteness assumptions from a theorem of Mandell. |
| title | $\mathbb{E}_{\infty}$-coalgebras and $p$-adic homotopy theory |
| topic | Algebraic Topology |
| url | https://arxiv.org/abs/2402.15850 |