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

doi:10.1007/s00222-018-0846-5

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

Mathematics

Research output: Contribution to journal › Article › peer-review

7 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 language	English
Pages (from-to)	215-240
Number of pages	26
Journal	Inventiones Mathematicae
Volume	216
Issue number	1
DOIs	https://doi.org/10.1007/s00222-018-0846-5
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)

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10.1007/s00222-018-0846-5

Cite this

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AU - Stapleton, Nathaniel

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

Abstract

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