Perfect complexes on finite flat affine groupoids

TL;DR

This paper characterizes the structure of perfect complexes on certain algebraic stacks by computing their Balmer spectrum and relating it to the cohomology ring's homogeneous spectrum.

Contribution

It provides a computation of the Balmer spectrum for perfect complexes on algebraic stacks with finite locally free covers, linking it to cohomology ring spectra.

Findings

Balmer spectrum identified with the homogeneous spectrum of the cohomology ring

Provides a description of perfect complexes on algebraic stacks

Connects algebraic geometry with spectrum theory

Abstract

We compute the Balmer spectrum of the category of perfect complexes on an algebraic stack admitting a finite locally free cover by an affine scheme and identify it with the homogeneous spectrum of the cohomology ring.