The Balmer spectrum of certain Deligne–Mumford stacks

2023/05/24 by Eike Lau · 2 citations
Mathematics · #Algebraic structures and combinatorial models #Algebraic Geometry and Number Theory #Homotopy and Cohomology in Algebraic Topology

paper · doi:10.1112/s0010437x23007200

Abstract

We consider a Deligne–Mumford stack X which is the quotient of an affine scheme \operatorname SpecA by the action of a finite group G and show that the Balmer spectrum of the tensor triangulated category of perfect complexes on X is homeomorphic to the space of homogeneous prime ideals in the group cohomology ring H^*(G,A) .

Cited by

• Permutation twisted cohomology, remixed
• Stratifying integral representations of finite groups
• The Balmer spectrum of integral permutation modules

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• The Balmer spectrum of certain Deligne-Mumford stacks
• Group actions on monoidal triangulated categories and Balmer spectra
• The Balmer spectrum of rational equivariant cohomology theories
• The Balmer spectrum of integral permutation modules
• Connectedness of the Balmer spectra of right bounded derived categories