Inventiones mathematicae

, Volume 208, Issue 1, pp 283–326 | Cite as

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

Article

Abstract

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.

Notes

Acknowledgments

We are very grateful to Neil Strickland, for the reasons explained above. We also thank John Greenlees and Mike Hill for several stimulating discussions.

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Copyright information

© Springer-Verlag Berlin Heidelberg 2016

Authors and Affiliations

  1. 1.Mathematics DepartmentUCLALos AngelesUSA
  2. 2.Department of Mathematical SciencesUniversity of CopenhagenCopenhagen ØDenmark

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