On the geometric fixed-points of real topological cyclic homology

Emanuele Dotto; Kristian J. Moi; Irakli Patchkoria

doi:10.1112/jlms.12862

On the geometric fixed-points of real topological cyclic homology

Emanuele Dotto, Kristian J. Moi, Irakli Patchkoria^* (Corresponding Author)

^*Corresponding author for this work

Mathematical Science

University of Warwick

Research output: Contribution to journal › Article › peer-review

Abstract

We give a formula for the geometric fixed-points spectrum of the real topological cyclic homology of a bounded below ring spectrum, as an equaliser of two maps between tensor products of modules over the norm. We then use this formula to carry out computations in the fundamental examples of spherical group-rings, perfect Fp-algebras, and 2-torsion free rings with perfect modulo 2 reduction. Our calculations agree with the normal L-theory spectrum in the cases where the latter is known, as conjectured by Nikolaus.

Original language	English
Article number	e12862
Number of pages	68
Journal	Journal of the London Mathematical Society
Volume	109
Issue number	2
Early online date	7 Feb 2024
DOIs	https://doi.org/10.1112/jlms.12862
Publication status	Published - Feb 2024

Bibliographical note

Open Access via the Wiley Agreement

Research funding
German Research Foundation. Grant Number: SPP 1768
Hausdorff Center for Mathematics
K&A Wallenberg Foundation

Data Availability Statement

No data availability statement.

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Cite this

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On the geometric fixed-points of real topological cyclic homology

Abstract

Bibliographical note

Data Availability Statement

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