On the geometric fixed-points of real topological cyclic homology
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arXiv
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| Main Authors: | , , |
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| Format: | Preprint |
| Published: |
2021
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| _version_ | 1866929248835469312 |
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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 |