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

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

doi:10.1007/s00222-018-0846-5

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

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Barthel, Tobias
Max Planck Institute for Mathematics, Max Planck Society;

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Nikolaus, Thomas
Max Planck Institute for Mathematics, Max Planck Society;

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Stapleton, Nathaniel
Max Planck Institute for Mathematics, Max Planck Society;

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https://doi.org/10.1007/s00222-018-0846-5
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arXiv:1709.04828.pdf
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Citation

Barthel, T., Hausmann, M., Naumann, N., Nikolaus, T., Noel, J., & Stapleton, N. (2019). The Balmer spectrum of the equivariant homotopy category of a finite abelian group. Inventiones Mathematicae, 216(1), 215-240. doi:10.1007/s00222-018-0846-5.

Cite as: https://hdl.handle.net/21.11116/0000-0003-D436-1

Abstract

For a finite abelian group $A$, we determine the Balmer spectrum of
$\mathrm{Sp}_A^{\omega}$, the compact objects in genuine $A$-spectra. This
generalizes the case $A=\mathbb{Z}/p\mathbb{Z}$ 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).