Adams-type maps are not stable under composition

Proceedings of the American Mathematical Society, Series B Pub Date : 2022-02-28 DOI:10.1090/bproc/137

Robert Burklund, Ishan Levy, Piotr Pstrkagowski

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Abstract

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 ∞ \mathbb {E}_{\infty } - k k -algebra is a transfinite composition of Adams-type maps.