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A slice refinement of Bökstedt periodicity Sulyma, Yuri
Description
Let $R$ be a perfectoid ring. Hesselholt and Bhatt-Morrow-Scholze have identified the Postnikov filtration on $\mathrm{THH}(R;\mathbb Z_p)$: it is concentrated in even degrees, generated by powers of the Bökstedt generator $\sigma$, generalizing classical Bökstedt periodicity for $R=\mathbb F_p$. We study an equivariant generalization, the \emph{regular slice filtration}, on $\mathrm{THH}(R;\mathbb Z_p)$. The slice filtration is again concentrated in even degrees, generated by $RO(\mathbb T)$-graded classes which can loosely be thought of as \emph{norms} of $\sigma$. The slices themselves are $RO(\mathbb T)$-graded suspensions of certain Mackey functors. When $R$ is $p$-torsionfree, the slice spectral sequence is concentrated in even degrees and collapses on the $E^2$ page.
Item Metadata
Title |
A slice refinement of Bökstedt periodicity
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Creator | |
Publisher |
Banff International Research Station for Mathematical Innovation and Discovery
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Date Issued |
2020-03-03T15:00
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Description |
Let $R$ be a perfectoid ring. Hesselholt and Bhatt-Morrow-Scholze have identified the Postnikov filtration on $\mathrm{THH}(R;\mathbb Z_p)$: it is concentrated in even degrees, generated by powers of the Bökstedt generator $\sigma$, generalizing classical Bökstedt periodicity for $R=\mathbb F_p$. We study an equivariant generalization, the \emph{regular slice filtration}, on $\mathrm{THH}(R;\mathbb Z_p)$. The slice filtration is again concentrated in even degrees, generated by $RO(\mathbb T)$-graded classes which can loosely be thought of as \emph{norms} of $\sigma$. The slices themselves are $RO(\mathbb T)$-graded suspensions of certain Mackey functors. When $R$ is $p$-torsionfree, the slice spectral sequence is concentrated in even degrees and collapses on the $E^2$ page.
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Extent |
68.0 minutes
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Subject | |
Type | |
File Format |
video/mp4
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Language |
eng
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Notes |
Author affiliation: Brown University
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Series | |
Date Available |
2020-09-21
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Provider |
Vancouver : University of British Columbia Library
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Rights |
Attribution-NonCommercial-NoDerivatives 4.0 International
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DOI |
10.14288/1.0394453
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URI | |
Affiliation | |
Peer Review Status |
Unreviewed
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Scholarly Level |
Postdoctoral
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Rights URI | |
Aggregated Source Repository |
DSpace
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Rights
Attribution-NonCommercial-NoDerivatives 4.0 International