A local-global principle for the telescope conjecture

TL;DR

This paper establishes a local-global principle for the telescope conjecture, demonstrating its validity for derived categories of Azumaya algebras, classifying stacks, and noetherian schemes, thus advancing understanding in algebraic geometry.

Contribution

It introduces an etale local-global principle for the telescope conjecture and applies it to broad classes of algebraic structures, providing new proofs and extending known results.

Findings

Proves the telescope conjecture for derived categories of Azumaya algebras on noetherian schemes

Establishes the conjecture for many classifying stacks and gerbes

Provides a new proof that the conjecture holds for noetherian schemes

Abstract

We prove an etale local-global principle for the telescope conjecture and use it to show that the telescope conjecture holds for derived categories of Azumaya algebras on noetherian schemes as well as for many classifying stacks and gerbes. This specializes to give another proof of the fact that the telescope conjecture holds for noetherian schemes.