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

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Markus Hausmann, Tobias Barthel, Niko Naumann, Thomas Nikolaus, Justin Noel, Nathaniel Stapleton

For a finite abelian group A, we determine the Balmer spectrum of the compact objects in genuine A-spectra. This generalizes the case A=Z/pZ due to Balmer and Sanders (Invent Math 208(1):283–326, 2017), 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 (Kuhn in Invent Math 157(2):345–370, 2004)
Original languageEnglish
JournalInventiones Mathematicae
Number of pages26
ISSN0020-9910
Publication statusE-pub ahead of print - 15 Dec 2019

ID: 211219206