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Proceedings of the American Mathematical Society

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Monadicity of the Bousfield-Kuhn functor


Authors: Rosona Eldred, Gijs Heuts, Akhil Mathew and Lennart Meier
Journal: Proc. Amer. Math. Soc. 147 (2019), 1789-1796
MSC (2010): Primary 55Q51
DOI: https://doi.org/10.1090/proc/14331
Published electronically: January 8, 2019
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Abstract: Let $ \mathscr {M}_n^f$ be the localization of the $ \infty $-category of spaces at the $ v_n$-periodic equivalences, the case $ n=0$ being rational homotopy theory. We prove that $ \mathscr {M}_n^f$ is for $ n\geq 1$ equivalent to algebras over a certain monad on the $ \infty $-category of $ T(n)$-local spectra. This monad is built from the Bousfield-Kuhn functor.


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Additional Information

Rosona Eldred
Affiliation: Max-Planck-Institut, Vivatsgasse 7, 53111 Bonn, Germany

Gijs Heuts
Affiliation: Mathematical Institute, Utrecht University, 3584CD Utrecht, The Netherlands

Akhil Mathew
Affiliation: Department of Mathematics, University of Chicago, Chicago, Illinois 60637-1514

Lennart Meier
Affiliation: Mathematical Institute, Utrecht University, 3584CD Utrecht, The Netherlands

DOI: https://doi.org/10.1090/proc/14331
Received by editor(s): March 29, 2018
Received by editor(s) in revised form: July 10, 2018
Published electronically: January 8, 2019
Additional Notes: This work was begun through a Junior Trimester Program at the Hausdorff Institute of Mathematics, and we thank the HIM for its hospitality.
The second author was supported by the European Research Council (ERC) under the European Union’s Horizon 2020 research and innovation programme (grant agreement no. 682922).
The third author was supported by the NSF Graduate Fellowship under grant DGE-114415 and was a Clay Research Fellow when this work was finished.
The fourth author was supported by DFG SPP 1786.
Communicated by: Mark Behrens
Article copyright: © Copyright 2019 American Mathematical Society