Français
Topological cyclic homology of the second truncated Brown–Peterson spectrum
Multi angle
Authors : Rognes, John (Author of the conference)
CIRM (Publisher )
19D50 - Computations of higher $K$-theory of rings, See Also {13D15,16E20}
19D55 - $K$-theory and homology; cyclic homology and cohomology, See also {18G60}
55P43 - Spectra with additional structure
55Q51 - vn-periodicity
CIRM (Publisher )
Loading the player...
|
Abstract :
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 $V(2)_* T C(B P\langle 2\rangle)$ 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 $-1 \leq * \leq 2 p^3+2 p^2+2 p-3$. Our computation is the first that exhibits chromatic redshift from pure $v_2$-periodicity to pure $v_3$-periodicity in a precise quantitative manner.
Keywords : Algebraic K-theory; elliptic cohomology; redshift; power operations
MSC Codes : Keywords : Algebraic K-theory; elliptic cohomology; redshift; power operations
19D50 - Computations of higher $K$-theory of rings, See Also {13D15,16E20}
19D55 - $K$-theory and homology; cyclic homology and cohomology, See also {18G60}
55P43 - Spectra with additional structure
55Q51 - vn-periodicity
|
Information on the Video
Film maker : Petit, JeanLanguage : English Available date : 17/02/2023 Conference Date : 26/01/2023 Subseries : Research talks arXiv category : Algebraic Topology Mathematical Area(s) : Topology Format : MP4 (.mp4) - HD Video Time : 01:05:19 Targeted Audience : Researchers ; Graduate Students ; Doctoral Students, Post-Doctoral Students Download : https://videos.cirm-math.fr/2023-01-26-rognes.mp4 
|
Information on the Event
Event Title : Chromatic Homotopy, K-Theory and Functors / Homotopie chromatique, K-théorie et foncteursEvent Organizers : Ausoni, Christian ; Hess Bellwald, Kathryn ; Powell, Geoffrey ; Touzé, Antoine ; Vespa, Christine Dates : 23/01/2023 - 27/01/2023 Event Year : 2023 Event URL : https://conferences.cirm-math.fr/2339.html
Citation Data
DOI : 10.24350/CIRM.V.19998203Cite this video as: Rognes, John (2023). Topological cyclic homology of the second truncated Brown–Peterson spectrum. CIRM. Audiovisual resource. doi:10.24350/CIRM.V.19998203 URI : http://dx.doi.org/10.24350/CIRM.V.19998203 |
See Also
- [Multi angle] Coinvariants, assembler K-theory, and scissors congruence / Author of the conference Zakharevich, Inna.
- [Multi angle] On the stable cohomology of the automorphism groups of free groups with coefficients / Author of the conference Vespa, Christine.
- [Multi angle] Representation spheres and chromatic Picard groups / Author of the conference Stojanoska, Vesna.
- [Multi angle] How algebraic is a stable model category? / Author of the conference Roitzheim, Constanze.
- [Multi angle] Equivalences in higher categories / Author of the conference Ozornova, Viktoriya.
- [Multi angle] (2)-categorical constructions and the multiplicative equivariant Barratt- Quillen-Priddy theorem / Author of the conference Osorno, Angélica.
- [Multi angle] Equivariant homotopy theory for infinite groups and THH with coefficients / Author of the conference Nikolaus, Thomas.
- [Multi angle] Equivariant elliptic cohomology / Author of the conference Meier, Lennart.
- [Multi angle] The universal property of topological Hochschild homology / Author of the conference Harpaz, Yonatan.
- [Multi angle] Prismatic and syntomic cohomology of ring spectra / Author of the conference Hahn, Jeremy.
- [Multi angle] Spaces of quasi-invariants / Author of the conference Berest, Yuri.
- [Multi angle] A survey of Mackey and Green 2-functors / Author of the conference Dell'Ambrogio, Ivo.
- [Multi angle] The chromatic Nullstellensatz / Author of the conference Burklund, Robert.
- [Multi angle] Adjoining roots to ring spectra and algebraic K-theory / Author of the conference Bayindir, Haldun Özgür.
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
Imagette Video
