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).
|Number of pages||26|
|State||Published - Apr 1 2019|
Bibliographical noteFunding 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.
© 2018, Springer-Verlag GmbH Germany, part of Springer Nature.
ASJC Scopus subject areas
- Mathematics (all)