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On the Balmer spectrum for compact Lie groups
Published online by Cambridge University Press: 14 November 2019
Abstract
We study the Balmer spectrum of the category of finite $G$-spectra for a compact Lie group $G$, extending the work for finite $G$ by Strickland, Balmer–Sanders, Barthel–Hausmann–Naumann–Nikolaus–Noel–Stapleton and others. We give a description of the underlying set of the spectrum and show that the Balmer topology is completely determined by the inclusions between the prime ideals and the topology on the space of closed subgroups of $G$. Using this, we obtain a complete description of this topology for all abelian compact Lie groups and consequently a complete classification of thick tensor ideals. For general compact Lie groups we obtain such a classification away from a finite set of primes $p$.
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- Research Article
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- © The Authors 2019
Footnotes
Current address: Max Planck Institute for Mathematics, Vivatsgasse 7, 53111 Bonn, Germany
Current address: Mathematical Institute, Rheinische Friedrich-Wilhelms-Universität Bonn, Endenicher Allee 60, 53115 Bonn, Germany
TB was supported by the Danish National Research Foundation Grant DNRF92 and the European Unions Horizon 2020 research and innovation programme under the Marie Sklodowska-Curie grant agreement No. 751794. JPCG is grateful to the EPSRC for support from EP/P031080/1. MH was supported by the Danish National Research Foundation Grant DNRF92.
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