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

TY - JOUR

T1 - The Balmer spectrum of the equivariant homotopy category of a finite abelian group

AU - Hausmann, Markus

AU - Barthel, Tobias

AU - Naumann, Niko

AU - Nikolaus, Thomas

AU - Noel, Justin

AU - Stapleton, Nathaniel

PY - 2019/12/15

Y1 - 2019/12/15

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).

M3 - Journal article

SN - 0020-9910

JO - Inventiones Mathematicae

JF - Inventiones Mathematicae

ER -