Cohomological descent for obstructions to local-global principle

TL;DR

This paper introduces a cohomological descent framework for understanding adelic points and obstructions to the local-global principle on algebraic stacks, leading to new obstructions and comparison results.

Contribution

It develops a formalism of cohomological descent for algebraic stacks, enabling the construction of new obstructions to the local-global principle.

Findings

New obstructions to local-global principle on algebraic stacks

Comparison results for obstructions on specific classes of stacks

Framework unifies adelic points and obstructions in a cohomological setting

Abstract

We develop a formalism of cohomological descent encoding adelic points and obstructions to local-global principle on algebraic stacks. As an application, by constructing new obstructions using the formalism, we obtain some comparison results of obstructions on some classes of algebraic stacks.