The spectrum of the equivariant stable homotopy category of a finite group

TY - JOUR

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

AU - Balmer, Paul

AU - Sanders, Beren

PY - 2017/4/1

Y1 - 2017/4/1

N2 - We study the spectrum of prime ideals in the tensor-triangulated category of compact equivariant spectra over a finite group. We completely describe this spectrum as a set for all finite groups. We also make significant progress in determining its topology and obtain a complete answer for groups of square-free order. For general finite groups, we describe the topology up to an unresolved indeterminacy, which we reduce to the case of p-groups. We then translate the remaining unresolved question into a new chromatic blue-shift phenomenon for Tate cohomology. Finally, we draw conclusions on the classification of thick tensor ideals.

AB - We study the spectrum of prime ideals in the tensor-triangulated category of compact equivariant spectra over a finite group. We completely describe this spectrum as a set for all finite groups. We also make significant progress in determining its topology and obtain a complete answer for groups of square-free order. For general finite groups, we describe the topology up to an unresolved indeterminacy, which we reduce to the case of p-groups. We then translate the remaining unresolved question into a new chromatic blue-shift phenomenon for Tate cohomology. Finally, we draw conclusions on the classification of thick tensor ideals.

U2 - 10.1007/s00222-016-0691-3

DO - 10.1007/s00222-016-0691-3

M3 - Journal article

SN - 0020-9910

VL - 208

SP - 283

EP - 326

JO - Inventiones Mathematicae

JF - Inventiones Mathematicae

IS - 1

ER -