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

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

Research output: Contribution to journalArticlepeer-review

10 Scopus citations

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 languageEnglish
Pages (from-to)215-240
Number of pages26
JournalInventiones Mathematicae
Volume216
Issue number1
DOIs
StatePublished - Apr 1 2019

Bibliographical note

Publisher Copyright:
© 2018, Springer-Verlag GmbH Germany, part of Springer Nature.

ASJC Scopus subject areas

  • General Mathematics

Fingerprint

Dive into the research topics of 'The Balmer spectrum of the equivariant homotopy category of a finite abelian group'. Together they form a unique fingerprint.

Cite this