Skip to Main Content

Proceedings of the American Mathematical Society Series B

Published by the American Mathematical Society since 2014, this gold open access, electronic-only journal is devoted to shorter research articles in all areas of pure and applied mathematics.

ISSN 2330-1511

The 2020 MCQ for Proceedings of the American Mathematical Society Series B is 0.95.

What is MCQ? The Mathematical Citation Quotient (MCQ) measures journal impact by looking at citations over a five-year period. Subscribers to MathSciNet may click through for more detailed information.

 

Adams-type maps are not stable under composition
HTML articles powered by AMS MathViewer

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.
Similar Articles
  • Retrieve articles in Proceedings of the American Mathematical Society, Series B with MSC (2020): 55T15
  • Retrieve articles in all journals with MSC (2020): 55T15
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