Comparing local-global obstructions on algebraic stacks

2026/08/03 by Chang Lv, Han Wu, Xucheng Zhang
Mathematics · #math.AG #math.NT #msc:14G12 #msc:14A20

paper · pdf

16 pages, git commit 20250823a/7496d3b

arxiv created 2026/08/03 · arxiv updated 2026/08/04

Abstract

For quotient stacks [X/G] with X a smooth quasi-projective geometrically integral k-variety and G a linear k-group, where k is a number field, we extend some relations between local-global obstructions on varieties, showing that étale-Brauer obstruction is the finest one among various obstructions (such as iterated descent, finite descent, descent, Brauer-Manin).

Citations

• Iterated descent obstructions for algebraic stacks
• The Brauer-Manin obstruction on algebraic stacks
• The second descent obstruction and gerbes
• Algebraic group actions on normal varieties
• Comparing descent obstruction and Brauer-Manin obstruction for open varieties
• Poitou-Tate without restrictions on the order
• Fundamental Groups of Algebraic Stacks