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On the strict Picard spectrum of commutative ring spectra

Part of: Cycles and subschemes Homotopy theory

Published online by Cambridge University Press:  28 July 2023

Shachar Carmeli
Shachar Carmeli*
Affiliation:
Department of Mathematical Sciences, University of Copenhagen, Universitetsparken 5, DK-2100 Copenhagen Ø, Denmark shachar.carmeli@gmail.com
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Abstract

We compute the connective spectra of maps from $\mathbb {Z}$ to the Picard spectra of the spherical Witt vectors associated with perfect rings of characteristic $p$. As an application, we determine the connective spectrum of maps from $\mathbb {Z}$ to the Picard spectrum of the sphere spectrum.

Keywords

ring spectrasphere spectrumPicard spectrumstrict unitshigher algebra

MSC classification

Primary: 55P43: Spectra with additional structure ($E_infty$, $A_infty$, ring spectra, etc.)
Secondary: 55P42: Stable homotopy theory, spectra 14C22: Picard groups

Information

Type
Research Article
Information
Compositio Mathematica , Volume 159 , Issue 9 , September 2023 , pp. 1872 - 1897
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Copyright
© 2023 The Author(s). The publishing rights in this article are licensed to Foundation Compositio Mathematica under an exclusive licence

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