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A preliminary report on the K(2)-local Picard group at p=2 Beaudry, Agnes
Description
The Picard group is an important invariant of a symmetric monoidal category. In the homotopy category of spectra, these are precisely the isomorphism classes of the n-spheres and the Picard group is a copy of the integers. However, after K(n)-localization, the Picard group can become much more complicated. The K(n)-local categories thus provide examples of interesting Picard groups. Their importance in chromatic homotopy theory is highlighted by the fact that the dualizing object for Brown-Commenetz duality comes from an invertible element. The K(n)-local Picard groups have been computed at all primes when n=1 and all odd primes when n=2. Mahowald predicted that the K(2)-local Picard group at the prime 2 would be very large in comparison to the situation at other primes. In this talk, I will explain why he was right and explain our current, although incomplete, understanding of the structure of this group. This project is joint work with Bobkova, Goerss and Henn.
Item Metadata
Title |
A preliminary report on the K(2)-local Picard group at p=2
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Creator | |
Publisher |
Banff International Research Station for Mathematical Innovation and Discovery
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Date Issued |
2016-05-01T09:01
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Description |
The Picard group is an important invariant of a symmetric monoidal category. In the homotopy category of spectra, these are precisely the isomorphism classes of the n-spheres and the Picard group is a copy of the integers. However, after K(n)-localization, the Picard group can become much more complicated. The K(n)-local categories thus provide examples of interesting Picard groups. Their importance in chromatic homotopy theory is highlighted by the fact that the dualizing object for Brown-Commenetz duality comes from an invertible element.
The K(n)-local Picard groups have been computed at all primes when n=1 and all odd primes when n=2. Mahowald predicted that the K(2)-local Picard group at the prime 2 would be very large in comparison to the situation at other primes. In this talk, I will explain why he was right and explain our current, although incomplete, understanding of the structure of this group.
This project is joint work with Bobkova, Goerss and Henn.
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Extent |
58 minutes
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Subject | |
Type | |
File Format |
video/mp4
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Language |
eng
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Notes |
Author affiliation: University of Chicago
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Series | |
Date Available |
2017-02-08
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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 |
10.14288/1.0320827
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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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Item Media
Item Citations and Data
Rights
Attribution-NonCommercial-NoDerivatives 4.0 International