On the geometric fixed-points of real topological cyclic homology

Fuente: arXiv
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Main Authors: Dotto, Emanuele, Moi, Kristian, Patchkoria, Irakli
Format: Preprint
Published: 2021
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author Dotto, Emanuele
Moi, Kristian
Patchkoria, Irakli
author_facet Dotto, Emanuele
Moi, Kristian
Patchkoria, Irakli
contents 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 $\mathbb{F}_p$-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.
format Preprint
id arxiv_https___arxiv_org_abs_2106_04891
institution arXiv
publishDate 2021
record_format arxiv
spellingShingle On the geometric fixed-points of real topological cyclic homology
Dotto, Emanuele
Moi, Kristian
Patchkoria, Irakli
Algebraic Topology
K-Theory and Homology
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 $\mathbb{F}_p$-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.
title On the geometric fixed-points of real topological cyclic homology
topic Algebraic Topology
K-Theory and Homology
url https://arxiv.org/abs/2106.04891