On the Balmer spectrum for compact Lie groups

Markus Hausmann; Tobias Barthel; John Greenlees

On the Balmer spectrum for compact Lie groups

Markus Hausmann, Tobias Barthel, John Greenlees

Institut for Matematiske Fag

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.

Originalsprog	Engelsk
Tidsskrift	arXiv.org
Udgave nummer	https://arxiv.org/abs/1810.04698
Status	Afsendt - 2019

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https://arxiv.org/abs/1810.04698

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title = "On the Balmer spectrum for compact Lie groups",

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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T1 - On the Balmer spectrum for compact Lie groups

AU - Hausmann, Markus

AU - Barthel, Tobias

AU - Greenlees, John

PY - 2019

Y1 - 2019

N2 - 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.

AB - 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.

M3 - Journal article

JO - arXiv.org

JF - arXiv.org

IS - https://arxiv.org/abs/1810.04698

ER -

On the Balmer spectrum for compact Lie groups

Abstract

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