Adams-type maps are not stable under composition
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We give a simple counterexample to the plausible conjecture that Adams-type maps of ring spectra are stable under composition. We then show that over a field, this failure is quite extreme, as any map to an E∞-k-algebra is a transfinite composition of Adams-type maps.
| Originalsprog | Engelsk |
|---|---|
| Tidsskrift | Proceedings of the American Mathematical Society, Series B |
| Vol/bind | 9 |
| Sider (fra-til) | 373-376 |
| DOI | |
| Status | Udgivet - 2022 |
Bibliografisk note
Funding Information:
Received by the editors March 7, 2022, and, in revised form, July 2, 2022. 2020 Mathematics Subject Classification. Primary 55T15. The second author was supported by the NSF Graduate Research Fellowship under Grant No. 1745302. 1In older literature, what we call descent-flat is often simply referred to as flat. We avoid the latter term as it is also often used to refer to maps such that π∗A → π∗B is flat, a much stronger condition than the one we work with.
Publisher Copyright:
© 2022 by the author(s).
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