The telescope conjecture for algebraic stacks

TL;DR

This paper proves the telescope conjecture for many algebraic stacks by utilizing generalized idempotents and also classifies the thick tensor ideals of perfect complexes on these stacks.

Contribution

It introduces a method to establish the telescope conjecture for algebraic stacks and classifies their thick tensor ideals, advancing understanding in algebraic geometry and tensor triangulated categories.

Findings

Proves the telescope conjecture for numerous algebraic stacks.

Classifies the thick tensor ideals of perfect complexes on stacks.

Provides a framework using generalized idempotents for these classifications.

Abstract

Using Balmer--Favi's generalized idempotents, we establish the telescope conjecture for many algebraic stacks. Along the way, we classify the thick tensor ideals of perfect complexes of stacks.