Abstract
For a finite abelian group A, we determine the Balmer spectrum of SpAω, 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 language | English |
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Pages (from-to) | 215-240 |
Number of pages | 26 |
Journal | Inventiones Mathematicae |
Volume | 216 |
Issue number | 1 |
DOIs | |
State | Published - Apr 1 2019 |
Bibliographical note
Funding Information:Justin Noel was partially supported by the DFG Grants: NO 1175/1-1 and SFB 1085—Higher Invariants, Regensburg. Niko Naumann and Nathaniel Stapleton were also partially supported by the SFB 1085—Higher Invariants, Regensburg. Tobias Barthel and Markus Hausmann were supported by the DNRF92.
Publisher Copyright:
© 2018, Springer-Verlag GmbH Germany, part of Springer Nature.
ASJC Scopus subject areas
- Mathematics (all)