The geometry of permutation modules

• 成果类型: Article
• 署名作者: Balmer, Paul; Gallauer, Martin
• 署名单位: University of California System; University of California Los Angeles
• 刊物名称: INVENTIONES MATHEMATICAE
• ISSN/ISSBN: 0020-9910
• DOI: 10.1007/s00222-025-01350-z
• 发表日期: 2025
• 页码: 841-928
• 关键词: TENSOR-TRIANGULAR GEOMETRY; homotopy category; BALMER SPECTRUM; NILPOTENCY

摘要

We consider the derived category of permutation modules for a finite group, in positive characteristic. We stratify this tensor triangulated category using Brauer quotients. We describe the spectrum of its compact objects, by reducing the problem to elementary abelian groups and then by using a twisted form of cohomology to express the spectrum locally in terms of the graded endomorphism ring of the unit. Together, these results yield a classification of thick and of localizing ideals.