English
Topological cyclic homology of the second truncated Brown–Peterson spectrum
Multi angle
Auteurs : Rognes, John (Auteur de la Conférence)
CIRM (Editeur )
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 (Editeur )
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Résumé :
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
Codes MSC : 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
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Informations sur la Vidéo
Réalisateur : Petit, JeanLangue : Anglais Date de publication : 17/02/2023 Date de captation : 26/01/2023 Sous collection : Research talks arXiv category : Algebraic Topology Domaine : Topology Format : MP4 (.mp4) - HD Durée : 01:05:19 Audience : Researchers ; Graduate Students ; Doctoral Students, Post-Doctoral Students Download : https://videos.cirm-math.fr/2023-01-26-rognes.mp4 
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Informations sur la Rencontre
Nom de la rencontre : Chromatic Homotopy, K-Theory and Functors / Homotopie chromatique, K-théorie et foncteursOrganisateurs de la rencontre : Ausoni, Christian ; Hess Bellwald, Kathryn ; Powell, Geoffrey ; Touzé, Antoine ; Vespa, Christine Dates : 23/01/2023 - 27/01/2023 Année de la rencontre : 2023 URL Congrès : https://conferences.cirm-math.fr/2339.html
Données de citation
DOI : 10.24350/CIRM.V.19998203Citer cette vidéo: 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 |
Voir aussi
- [Multi angle] Coinvariants, assembler K-theory, and scissors congruence / Auteur de la Conférence Zakharevich, Inna.
- [Multi angle] On the stable cohomology of the automorphism groups of free groups with coefficients / Auteur de la Conférence Vespa, Christine.
- [Multi angle] Representation spheres and chromatic Picard groups / Auteur de la Conférence Stojanoska, Vesna.
- [Multi angle] How algebraic is a stable model category? / Auteur de la Conférence Roitzheim, Constanze.
- [Multi angle] Equivalences in higher categories / Auteur de la Conférence Ozornova, Viktoriya.
- [Multi angle] (2)-categorical constructions and the multiplicative equivariant Barratt- Quillen-Priddy theorem / Auteur de la Conférence Osorno, Angélica.
- [Multi angle] Equivariant homotopy theory for infinite groups and THH with coefficients / Auteur de la Conférence Nikolaus, Thomas.
- [Multi angle] Equivariant elliptic cohomology / Auteur de la Conférence Meier, Lennart.
- [Multi angle] The universal property of topological Hochschild homology / Auteur de la Conférence Harpaz, Yonatan.
- [Multi angle] Prismatic and syntomic cohomology of ring spectra / Auteur de la Conférence Hahn, Jeremy.
- [Multi angle] Spaces of quasi-invariants / Auteur de la Conférence Berest, Yuri.
- [Multi angle] A survey of Mackey and Green 2-functors / Auteur de la Conférence Dell'Ambrogio, Ivo.
- [Multi angle] The chromatic Nullstellensatz / Auteur de la Conférence Burklund, Robert.
- [Multi angle] Adjoining roots to ring spectra and algebraic K-theory / Auteur de la Conférence Bayindir, Haldun Özgür.
Bibliographie
- 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
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