A chromatic vanishing result for TR
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- by Liam Keenan and Jonas McCandless;
- Proc. Amer. Math. Soc. 152 (2024), 3705-3713
- DOI: https://doi.org/10.1090/proc/16840
- Published electronically: July 1, 2024
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Abstract:
In this note, we establish a vanishing result for telescopically localized topological restriction homology TR. More precisely, we prove that $T(k)$-local TR vanishes on connective $L_n^{p,f}$-acyclic $\mathbb {E}_1$-rings for every $1 \leq k \leq n$ and deduce consequences for connective Morava K-theory and the Thom spectra $y(n)$. The proof relies on the relationship between TR and the spectrum of curves on K-theory together with fact that algebraic K-theory preserves infinite products of additive $\infty$-categories which was recently established by Córdova Fedeli [Topological Hochschild homology of adic rings, Ph.D. thesis, University of Copenhagen, 2023].References
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Bibliographic Information
- Liam Keenan
- Affiliation: Department of Mathematics, University of Minnesota, 206 Church Street SE, Minneapolis, Minnesota 55455
- Email: keena169@umn.edu
- Jonas McCandless
- Affiliation: Max Planck Institute for Mathematics, Vivatsgasse 7, 53111 Bonn, Germany
- Email: mccandless@mpim-bonn.mpg.de
- Received by editor(s): November 30, 2023
- Received by editor(s) in revised form: January 22, 2024, and February 20, 2024
- Published electronically: July 1, 2024
- Additional Notes: The second author was funded by Max Planck Institute for Mathematics in Bonn and the Deutsche Forschungsgemeinschaft (DFG, German Research Foundation) under Germany’s Excellence Strategy EXC 2044 390685587, Mathematics Münster: Dynamics-Geometry-Structure while working on this project.
- Communicated by: Julie Bergner
- © Copyright 2024 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 152 (2024), 3705-3713
- MSC (2020): Primary 19D55, 55P42
- DOI: https://doi.org/10.1090/proc/16840
- MathSciNet review: 4781967