On the Balmer spectrum for compact Lie groups

Research output: Contribution to journalJournal articleResearch

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.
Original languageEnglish
JournalarXiv.org
Issue numberhttps://arxiv.org/abs/1810.04698
Publication statusSubmitted - 2019

ID: 211219271