Iterated descent obstructions for algebraic stacks

TL;DR

This paper proves that for certain algebraic stacks over number fields, the descent obstruction is equivalent to the iterated descent obstruction, simplifying the understanding of rational points on these stacks.

Contribution

It establishes the equality of descent and iterated descent obstructions for a broad class of algebraic stacks over number fields.

Findings

Descent obstruction equals iterated descent obstruction for smooth separated stacks.

Equality holds for stacks with finite étale coverings of smooth geometrically integral varieties.

Results simplify the analysis of rational points on algebraic stacks.

Abstract

Base on a conjecture, we prove that for any smooth separated stack of finite type over a number field, its descent obstruction equals its iterated descent obstruction. As a consequence, we show that for any algebraic stack over a number field that has a finite etale covering of a smooth geometrically integral variety, its descent obstruction equals its iterated descent obstruction.