TY - JOUR
T1 - The Balmer spectrum of the equivariant homotopy category of a finite abelian group
AU - Barthel, Tobias
AU - Hausmann, Markus
AU - Naumann, Niko
AU - Nikolaus, Thomas
AU - Noel, Justin
AU - Stapleton, Nathaniel
N1 - Publisher Copyright:
© 2018, Springer-Verlag GmbH Germany, part of Springer Nature.
PY - 2019/4/1
Y1 - 2019/4/1
N2 - 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).
AB - 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).
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U2 - 10.1007/s00222-018-0846-5
DO - 10.1007/s00222-018-0846-5
M3 - Article
AN - SCOPUS:85058553682
SN - 0020-9910
VL - 216
SP - 215
EP - 240
JO - Inventiones Mathematicae
JF - Inventiones Mathematicae
IS - 1
ER -