On the Balmer spectrum for compact Lie groups
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On the Balmer spectrum for compact Lie groups. / Barthel, Tobias; Greenlees, John; Hausmann, Markus.
I: Compositio Mathematica, Bind 156, Nr. 1, 2020, s. 39-76 .Publikation: Bidrag til tidsskrift › Tidsskriftartikel › fagfællebedømt
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TY - JOUR
T1 - On the Balmer spectrum for compact Lie groups
AU - Barthel, Tobias
AU - Greenlees, John
AU - Hausmann, Markus
PY - 2020
Y1 - 2020
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.
U2 - 10.1112/S0010437X19007656
DO - 10.1112/S0010437X19007656
M3 - Journal article
VL - 156
SP - 39
EP - 76
JO - Compositio Mathematica
JF - Compositio Mathematica
SN - 0010-437X
IS - 1
ER -
ID: 211219271