Chromatic Homotopy, K-Theory and Functors / Homotopie chromatique, K-théorie et foncteurs

Collection Chromatic Homotopy, K-Theory and Functors / Homotopie chromatique, K-théorie et foncteurs

Organizer(s) Ausoni, Christian ; Hess Bellwald, Kathryn ; Powell, Geoffrey ; Touzé, Antoine ; Vespa, Christine

Date(s) 23/01/2023 - 27/01/2023

linked URL https://conferences.cirm-math.fr/2339.html

00:00:00 / 00:00:00

13 15

Topological cyclic homology of the second truncated Brown–Peterson spectrum

In joint work with Gabriel Angelini-Knoll, Christian Ausoni, Dominic Leon Culver and Eva Höning, we calculate the $\bmod \left(p, v_1, v_2\right)$ homotopy $V(2)_² T C(B P\langle 2\rangle)$ of the topological cyclic homology of the truncated Brown-Peterson spectrum $B P\langle 2\rangle$, at all primes $p \geq 7$, and show that it is a finitely generated and free $\mathbb{F}_p\left[v_3\right]$-module on $12 p+4$ generators in explicit degrees within the range $-1 \leq ² \leq 2 p^3+2 p^2+2 p-3$. Our computation is the first that exhibits chromatic redshift from pure $v_2$-periodicity to pure $v_3$-periodicity in a precise quantitative manner.

Information about the video

Date of recording 26/01/2023
Date of publication 17/02/2023
Institution CIRM
Licence CC BY NC ND
Language English
Audience Researchers, Graduate Students
Director(s) Jean Petit
Format MP4

Citation data

DOI 10.24350/CIRM.V.19998203
Cite this video Rognes, John (26/01/2023). Topological cyclic homology of the second truncated Brown–Peterson spectrum. CIRM. Audiovisual resource. DOI: 10.24350/CIRM.V.19998203
URL https://dx.doi.org/10.24350/CIRM.V.19998203

Domain(s)

Algebraic Topology

Bibliography

ANGELINI-KNOLL, Gabriel, AUSONI, Christian, CULVER, Dominic Leon, et al. Algebraic K-theory of elliptic cohomology. arXiv preprint arXiv:2204.05890, 2022. - https://arxiv.org/pdf/2204.05890.pdf

MSC codes

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