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

• 成果类型: Article
• 署名作者: Balmer, Paul; Sanders, Beren
• 署名单位: University of California System; University of California Los Angeles; University of Copenhagen
• 刊物名称: INVENTIONES MATHEMATICAE
• ISSN/ISSBN: 0020-9910
• DOI: 10.1007/s00222-016-0691-3
• 发表日期: 2017
• 页码: 283-326
• 关键词: tate cohomology; SUBCATEGORIES; localization; bousfield

摘要

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.