The Balmer spectrum of the equivariant homotopy category of a finite abelian group

For a finite abelian group \(A\), we determine the Balmer spectrum of \(\mathrm{Sp}_A^{\omega}\), the compact objects in genuine \(A\)-spectra. This generalizes the case \(A=\mathbb{Z}/p\mathbb{Z}\) due to Balmer and Sanders \cite{Balmer-Sanders}, by establishing (a corrected version of) their log\(...

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Bibliographic Details
Published in:arXiv.org 2018-12
Main Authors: Barthel, Tobias, Hausmann, Markus, Naumann, Niko, Thomas, Nikolaus, Noel, Justin, Stapleton, Nathaniel
Format: Article
Language:English
Subjects:
Fixed points (mathematics)
Group theory
Online Access:Get full text
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Summary:For a finite abelian group \(A\), we determine the Balmer spectrum of \(\mathrm{Sp}_A^{\omega}\), the compact objects in genuine \(A\)-spectra. This generalizes the case \(A=\mathbb{Z}/p\mathbb{Z}\) due to Balmer and Sanders \cite{Balmer-Sanders}, by establishing (a corrected version of) their log\(_p\)-conjecture for abelian groups. We also work out the consequences for the chromatic type of fixed-points and establish a generalization of Kuhn's blue-shift theorem for Tate-constructions \cite{kuhn}.
ISSN:2331-8422
DOI:10.48550/arxiv.1709.04828