Adams-type maps are not stable under composition
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- by Robert Burklund, Ishan Levy and Piotr Pstragowski HTML | PDF
- Proc. Amer. Math. Soc. Ser. B 9 (2022), 373-376
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 $\mathbb {E}_{\infty }$-$k$-algebra is a transfinite composition of Adams-type maps.References
- J. F. Adams, Stable homotopy and generalised homology, Chicago Lectures in Mathematics, University of Chicago Press, Chicago, Ill.-London, 1974. MR 0402720
- H. Cartan, Algèbres d’Eilenberg-MacLane et Homotopie, Exposés 2 à 16, Séminaire Henri Cartan, Ecole Normale Supérieure, Paris (1956).
- Ethan S. Devinatz, Morava modules and Brown-Comenetz duality, Amer. J. Math. 119 (1997), no. 4, 741–770. MR 1465068, DOI 10.1353/ajm.1997.0023
- Irakli Patchkoria and Piotr Pstragowski, Adams spectral sequences and Franke’s algebraicity conjecture, Preprint arXiv:2110.03669, 2021.
Additional Information
- Robert Burklund
- Affiliation: Department of Mathematical Sciences, University of Copenhagen, Denmark
- MR Author ID: 1404637
- Email: rb@math.ku.dk
- Ishan Levy
- Affiliation: Department of Mathematics, MIT, Cambridge, Massachusetts
- ORCID: 0000-0002-4593-7839
- Email: ishanl@mit.edu
- Piotr Pstragowski
- Affiliation: Department of Mathematics, Harvard, Cambridge, Massachusetts
- MR Author ID: 1455554
- Email: pstragowski.piotr@gmail.com
- Received by editor(s): March 7, 2022
- Received by editor(s) in revised form: July 2, 2022
- Published electronically: August 30, 2022
- Additional Notes: The second author was supported by the NSF Graduate Research Fellowship under Grant No. 1745302.
- Communicated by: Julie Bergner
- © Copyright 2022 by the authors under Creative Commons Attribution-NonCommercial 3.0 License (CC BY NC 3.0)
- Journal: Proc. Amer. Math. Soc. Ser. B 9 (2022), 373-376
- MSC (2020): Primary 55T15
- DOI: https://doi.org/10.1090/bproc/137
- MathSciNet review: 4477146